I never quit battles unless I get annoyed with the AI (eg Mongols attack me on campaign map then camp up a hill). The reason I quit that siege was that there was no way for my units to get into the city, as once pratically all my infantry were killed all I had left were Cavalry Militia, which couldn't use the ladders - nothing to do but run down the timer.
I actually enjoy losing battles, either because its nice to get beaten fairly by the AI (rare though that is), or because it tends to be a last man stand against some giant Mongol/Timurid/Aztec army.
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