War is hell.
I've started prefacing a lot of my answers about warfare that way. "War is hell." It seems like an important reminder when it comes to warfare in fictional worlds. We often develop romantic visions of what warfare should be. War is not those visions. War is vicious, dirty, and very very permanent. A real nation will not go to war until it is the very last option because their leaders know that, once war is declared, there will be women whose husbands will not come home. There will be children who will never meet their father. War is not taken lightly, ever.
This makes questions like this an interesting challenge. At first glance, this concept of the War Hero is an absurdity -- a romantic gesture to a kind of warfare that may have never actually existed in the first place. No nation today would ever consider anything remotely similar to a War Hero. This is the crux of the challenge. To make a believable War Hero tradition, we need to build a national culture which is not remotely similar to our own. We need to build a nation such that the concept of the War Hero actually works for them.
No nation keeps a wartime ritual which doesn't benefit them for long. If your enemy realizes you have a ritual which doesn't benefit you, they will exploit this as deeply as they can. An excellent example of this is the reign of Shaka Zulu. At the time of his rise to power, the tribes of the region had a highly ritualized form of warfare. There was little loss of life. Shaka turned that all on its head, bringing forth a very brutal form of warfare that the ritual-warriors were simply not ready for. As a result, there are no ritualized wars in that region any more. The rituals no longer benefit them, so they have been purged. You have not specified much of your world, so it's plausible that the other nations have similar rituals. Perhaps it is forbidden to attack an enemy's War Hero directly unless you, yourself, are your nation's War Hero. If so, that would solve your situation. If not, we have to dig deeper.
Your position of requiring the War Hero to inhabit the front lines, where life expectencies are short is quite unusual for individuals whose life brings great morale. Typically these individuals are put on display for morale purposes quite far from actual danger for the exact reasons you are concerned: their death is a brutal moral blow. Thomo raises the fictional example of Katniss from The Hunger Games. Once she becomes a symbol, she is pulled away from danger as much as possible. This sort of behavior has occurred in real life as well. There's plenty of non-fiction about the military career of Elvis Presley, who actually provides a lot of insight into how these morale builders fit into the front lines.
Elvis and his military career is a fascinating topic. I admit to having only done cursory study of his time in the Army, but even the little I have read is amazing. He was given his draft notice on December 8, 1957, and chose to act as a normal soldier rather than an entertainer, just like your War Hero. Perhaps "chose" is a bit too strong of a word. His manager, Colonel Tom Parker, had written the government in '56 requesting "Special Services" for Elvis. Special Services was the "celebrity cop out," which let you do basic training for six months, then return to normal life. All you had to do was a few shows for the Army every year. However, Parker had no intention of Presley serving in Special Services. Those Army shows were free, and Parker had no intention of giving up free shows to anyone. Parker knew that Elvis was actually developing a bit of a bad rap, and needed a boost. He convinced Elvis to refuse Special Services, and instead become a normal solder. This refusal of Special Services was intended as a ploy to garner support from those who thought Elvis was damaging the moral fabric of society. Apparently this infuriated Elvis, but this kind of stunt is exactly what you pay a manager for. (It also worked. Elvis came back from the war to a huge new demographic of supporters and fans!)
We can see the first attempts to keep our "War Hero" off the front lines right away. Both the Army and Navy immediately extended offers to simply perform instead of fight. The Pentagon itself actually extended offers of Special Services. But Elvis refused (which was all part of the story Parker was weaving). Elvis announced he was going to be a normal soldier, and that was that. So what's a military to do? They sent him to Germany to fight, like the rest of the soldiers. Once he got there, General Randal offered him Special Services one more time. When he refused, they assigned him as a driver to Captain Russel of the 3rd armored. Driving a captain around is pretty safe work. Generally speaking, the captains know not to put their own lives at risk, so Elvis' life was naturally out of harm's way. This job lasted until Russel got tired of the attention that surrounded Elvis, and transferred him to be the driver for Sergent Ira Jones. Sergeants have to go more in harm's way than a captain, but you still see a level of safety to the jobs handed to Elvis.
Now all accounts suggest that Elvis shirked no duty. He went out there and did his job, like any other warrior of the day. Some even say he did more, trying to prove that he wasn't relying on his fame. But, in the end, I find no records of Elvis being put in especially precarious positions. You keep your stars safe. Maybe you can adjust your War Hero story to align more with Elvis' story. If not, what about another hero, Manfred von Richthofen?
Von Richthofen is most often known by his nickname, The Red Barron. He is credited with 80 air combat victories in his career. It is noted that he, despite being an aggressive fighter pilot, was actually quite careful. Rather than relying on extraordinary flying or taking risks, his focus was on assured victories. He followed Dicta Boelche, a tactical theory by ace Oswald Boelche. The goal was not to win as many fights as possible, but rather to make sure that when you do fight, you don't lose. This kept him alive and well for many years. This sort of mindset would be a very valuable one for a War Hero, and the Red Baron showed that you can do it and stay on the front lines.
By 1918, von Richthofen was actually enough of a hero that the government of Germany worried about the morale impacts of his possible death in combat. He was offered a ground job, but refused, arguing it was his duty to fight in the air. He held this attitude until shot down on April 21, 1918. My research does not show whether the feared morale hits actually took place in Germany, but it does show that he was burred by the Allies, who recovered his body, with full honors.
The Red Baron's story is pretty much only possible because of the novelty of air combat in the day. This was a strange time where one person really could make a difference in a war, because there simply weren't many pilots out there flying. Perhaps you can give your War Hero one of these new fangled machines of war. If you can't find a good new tool for him to use, we have to get our hands dirty. We have to make a culture. All the easy solutions are gone.
So you have a culture that really needs the War Hero to go risk their lives, even though everyone knows its a huge morale bust when they die (as they inevitably do). How do you make this a reality which doesn't become just another ritual removed from service after it failed to be useful. We need to find a way to create a culture such that the benefits of the War Hero outweigh the costs. Naturally, the only way this happens is if the War Hero's morale bonus outweighs the pain of his loss. The War Hero needs to provide a substantial benefit while he's alive, or we need to be able to reduce the pain of his death.
We're going to need a culture where a front-line soldier can be important. This is unusual. Typically front-line soldiers are sent to the front lines because they are less important than those who have spent more time learning military science, like officers. We need an army structure where a front-line soldier's opinions can matter, but typically don't matter. If they always mattered, nothing would be special.
At this point, all that can be done is brainstorm. What follows is one idea which might work, one of many. As long as you follow the principles of the War Hero doing more good than harm, any idea can work. This is simply one that I can see occurring in some societies.
I'd suggest a culture with a very strong hierarchical structure to it. There should be a strong suppression of creative solutions from the front-line soldiers. This culture should have a strong "this is how we've always done it" vibe. They should have methodical solutions that they follow to a fault. This sort of lack of creativity is typically a strong determent in warfare, but it may stem from how the society has developed in times of peace.
This opens the door for the War Hero to be a repressed front-line individual who is given an opportunity to have people listen to him or her for the first time. As long as the existing solutions are working, a War Hero is pointless. One just follows the solutions they always followed. However, when the old solutions are failing, a War Hero might be this society's way of breaking free of their mold.
In this approach, the War Hero is given the opportunity to describe how he or she wishes to be used. This gives them an opportunity to demonstrate a new approach to combat that the officers simply aren't trying.
This might actually be very effective against an opponent. If you know that this culture isn't creative in their solutions, relying on the same tactics every time, you may get lazy and reliant on them to do the same thing. Suddenly this War Hero may topple your theories, and win several victories.
In this mythos, the War Hero would have two phases of existence. While the War Hero is alive, we get to see how well they can stay alive. A good War Hero will stay alive long enough to show everyone what new fangled ideas about warfare he or she has. Presumably you would pick one which has this potential. They then show everyone a new way of doing combat until they die. When they die, people mourn the death of the War Hero, but the second phase of their existence begins. Now it is the solemn duty of the officers who observed the War Hero to incorporate their novel thinking into their strategies. In this way, while the physical War Hero dies, their legacy lives on as the culture's entire approach to warfare adapts to incorporate this thinking.
Now this is a pretty extreme solution. Most modern cultures are smart enough to accept new good ideas more than once per generation. However, if you craft your culture correctly, this unusual pattern may be very reasonable. If you see this highly polarized approach to innovation in normal peaceful life, then it would be reasonable to see the military adapt this style into their combat.
Its simply up to you to create a culture where this War Hero approach isn't absurd. Good luck!