Battery Question

I am truly a newbie when it comes to the Airstream. We purchased our first one in December of 2014 and have been out twice. It is a 2015 27FB. I noticed that once we got it home and were getting it ready for the first outing, the battery was dead. Since I have a 30 AMP circuit at my home, i place the battery switch to the in use position and 24 hours later the battery seemed to be fine. I did find however, that the water levels in one of the batteries was really low....no problem added distilled water to the correct level. When we went on our second trip, I once again did not check for the batteries until we went to depart and checked the fridge to make sure it was on propane and low and behold.....all power to the coach was dead....no lights...nothing. (I am still trying to build a comprehensive pre departure checklist...lol) After camping for three days, I tried to test the battery again, and this time when I switched to battery power it showed 12.8 but quickly went to 12.4 and stabilized there.?? I returned to shore power for the remainder of the trip. Upon arriving home, I left my 30 AMP plug off for about 3 hours and then checked the battery again and this time it was 12.7 steady...water level low again. I am beginning to wonder if the original batteries might already be bad and if I should replace with to AGM batteries? If so, what AGM batteries have you all used. Any thoughts? I am pulling it back to to the dealer on Monday to have the full awning package installed.