You may want to move this post to TECHTALK...
Have you eliminated any 12volt loads that may be draining the battery over night? (lights, fans....). Are the battery cable connections tight? Have you checked the battery water level?
Check the date code on the battery. Just to insure they did not slip you an older battery that has been on the shelf for a long time. Log on to the battery mfr website and check where they put the date code (usually on or around a terminal) and how to read them.
One other thing you may try, is after you charge the battery, disconnect the shore power, and take a voltage reading then pull the main fuse by the battery. In the morning check to see if the battery held a charge, if it held a charge then you have something in the TT draining the battery. If it did not hold a charge then it is the battery. I would then take it (TT) back to the dealer as soon as possible, and get them to replace the battery. Give them a call! Tell them that it has not held a charge since DAY 1.
The only other item I can think of is if the BREAK AWAY SWITCH cable was accidentally pulled (activated), that energizes the electric brakes. Check the cable to it to see if it is warm. Probably not the problem, but check it anyway.
Odds are the battery is no longer going to hold a useable charge, after being drained so many times.
Let us know what you find.
2013 Jayco Eagle 284BHS
250Watt Grape Solar Panel, MorningStar MPPT 60 Charge Controller
1500 Watt Ramsond PSI, 2 Trojan T145 Batteries (260Ah)
2 - AirSight Wireless IP Cameras (used as rear view cameras)
EnGenius WI-FI extender, D-Link wireless (n) modem
MagicJack Internet Phone
2012 Ford F150XLT, EcoBoost w/3.73
157" Wheel base, HD Towing Package
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