(i am very sorry. I am writing from a different browser than usually, and this one has a German spelling correction, that messes with my writing. I am sorry for the many spelling and capitalization mistakes)
Another historical example is the Thirty years war. The war was started for religious and political reasons. In those days, most countries had a Standing army. So in the first years of the war, it just "went fine". No side could get a significant advantage.
After a few years, the governments started Recruiting new soliders. In those days, a soldier would get a one-time-payment once they were hired, and regular payments afterwars, as well as (sometimes) a one-time-payment when he was dismissed.
After another dozen years of war, economy in most countries involved was at a harsh low. The governments were pretty much bankrupt, only being able to continue to wage war because they would conquer and loot cities and use the loot to pay their armies. Often, soldiers were not paid for long times, leading to deserters and marauders.
What arose was "the Monster of war", a "beast that keeps itself alive". If for example sweden and Austria would have wanted to go to peace, they would Need Money to pay their soldiers. Money that they didn't have anymore. So in order to make peace, the other Party would have needed to pay them some Money, so they could retire their armies. But the other parties were also bancrupt, and it would have been a BIG disgrace to admit that you actually couldn't pay that Money. You would need to pretent you could, but don't WANT to. So everyone waited for the tides of war to turn, so next time you negotiated for peace, you were in a better Position and could request Money from the other guys.
Everyone wanted to go to peace, noone could afford to do so. Meanwhile, the soldiers were poorly equipped, starving, most often only being kept alive by looting the local farmers and villages. In those days, you couldn't fight during winter, so during the winter months, armies were sent to quarters. Now, a huge german City like Frankfurt hat 80-100k citizens. The armies were equally huge. No single City could Support a whole army, so in late fall, armies were disbanded and spread over a large area - preferably an area that belongs to your enemy, because in spring, everything edible, huntable, rapeable or forageable would be gone or dead. As you may easily imagine, after 30 years of war, the countries were barren and dead. So in order to Keep your army alive - you placed it in some neighbours land. Even if he didn't have anything to do with the war (yet). Also, those cities still had some wealth, that you could use to fuel the war...
And so, the involved parties became more and more, forming a complex System of alliances, secret treaties and pacts, that basically ensured that no side would ever win.
And then there was France. France profited from the other countries being at each others throat, and just continued changing alliances and Support whenever one Party was about to lose. THus, they acutally made sure the war continued.
But why wasn't the war decided in battle? Because of the way warfare worked. In a battle, only around 10% of all soldiers who stopped fighting were actually dead. Many were wounded, not necessary gravely, but most had simply fled the battlefield. Breaking morale was the main thing that scattered armies. But later, they would Reform. And while the losses were harsh, there was an abundance of new soldiers to "recruit", and muskets were so simple, that you didn't require much training. So even after you won a battle, the very same army could try to fight you again only few weeks later. Also, the armies were so huge, that usually withdrawing from the field was easy for the commanders and high-ranking officers. So your command staff stayed alive for many many battles, and they were the only thing that, if lost,could have permanently scattered an army.
The thirty years war is an excellent example of a war that couldn't be stopped anymore. You might take the "lessons learned" from that war, and try to fit them into the Scenario you have in mind. But the Basic mechanisms should be clear:
- It's too expensive to stop the war
- No side can gain a clear Advantage
- You'd loose face by admitting defeat or financial difficulties
- Ever growing battlefield, so new parties join the war, changing the tides of battle
- Third parties wanting to keep the war alive.