1. Did your "new" battery start the APU? Does your APU require a 12 volt battery to start it?
2. APU's(gensets) do NOT have a charge circuit. The battery charge is part of the Trailer Power Converter. So, if the battery was low and had enough to start the genset, but the Trailer Power Converter is either defective or the fuse is blown, that means your battery was not receiving a charge and the APU would draw it down as well as anything running in the trailer
3. Slow recharge the battery and then have it load tested. The odds are the battery is OK and the problem is in your Trailer charge system. Doug