I have to disagree in parts here, Louis. I don't think it's rude or disrespectful if one player chooses to fight on. It always depends on the overall situation. Also the argument about different timezones doesn't hold much value, whoever started a game at 10 pm should know it could drag on... Same goes for peeps still online at 4am, their choice...
I don't think you can liken MTW to chess, for various reasons (most of all the random nature of encounters, you cannot really make a move and take the enemy's piece like in chess, because just against the odds, the enemy unit might win. As such, you cannot plan several moves ahead with certainty as you would do in a chess game), MTW battles aren't turn based and not necessarily the best strategist wins, but also a cheap rusher or a person who just can click faster than you.
But anyway, about routing, it's up to oneself, really, but if the majority of the other players (even your allies)involved in the game start telling you to give it up, it's worth to reconsider. I don't want to see whole armies rout, but as said before, if you have just two or three depleted units left, you can safely rout them and don't fear to lose honour by denying your opponents the pleasure of routing them by themselves.

For those who rout whole armies, at least make it a challenge by choosing to withdraw instead and trying to cover it with part of your forces. This would be a challenge for both sides. If you manage to escape with a large percentage of your forces, you might feel a sense of accomplishment.