Battery dead:won't charge

That does happen a lot, but its more from the lack of a proper recharging rather then the discharging itself.  Problem is that you need a full 24-48 hours of current going in one direction only (into the battery) to prevent sulfation of the plates.   I've also found that slow charging is the only way to recover a really low battery, 2A, and 48 hours.  While actively camping that's a little difficult to do.  You almost need to pull the battery out and charge it elsewhere.  The batteries can't handle lots of charge current when they are low, as a matter of fact you should never charge a lead-acid with more than a couple of amps.   I don't think you have the choice with the on-board charger, and if you did have the choice, you'd be pulling current from the battery under load and making the sulfation worse.   

I deal with lots of battery chemistry - and it really doesn't get less confusing.  But it's handy to reference this place for good info:

Batteries are funny - how about this one - you have a li-ion in your phone/drill/ipad?  If you ever charge those while they are really cold they will die forever.  Fun.