Cultural Norms
For instance, all men must serve as guard in a place, and it rotates out to different people, but the custom is that you are considered an arm of the law not an individual, so the custom is that you never lower your faceplate or say your name when you serve. Some take this more seriously than others--the more seriously they take it the more likely they are to follow this custom to the letter.
The sacred vow.
He made a promise, and will not remove it until the promise is met.
Psychological problems
Paranoia, feeling naked without the armor, delusions that the armor is a part of their soul...you pick...
Magical Reasons
Mundane is best but...perhaps he's an elite solider of the king's army. Out of armor he's a paraplegic. To be able to move around properly he has to wear it fully.
The helmet is stuck or bent into place
A la A Knight's Tale the movie. When the main character masqueraded as a knight, he used the fact that the helmet was bent not to be able to remove it.
A face that only a mother could love
Character mentions that they are deformed, but respected as a knight and so never removes helmet in front of people.
However, if:
You're curious why he doesn't remove his armor, but you don't want to ask for fear of being rude.
Then no reason would be given in the first place, correct? And this is not about the ACTUAL reason, but the excuse given or how it's passed off, yes?
So going to say--
Everyone around you accepts it
"Him? That's just Sir Larry. Pay 'em no heed. He comes in every night."
"Why does he keep his armor on?" you ask.
"Been that way since the war. He saved the village, so Sir Larry does what he pleases," the barkeep answers.