I have a 1968 PA31-310 Navajo with an aftermarket AC unit that uses what I believe is about a 40 amp motor to drive the compressor. The battery is a 17amp hr wet Gill that's 2.8 yrs old. The alternators are 50 amp. Last friday it was so hot I had to run the AC continuously at cruise altitude of 6500ft. I noticed that my ammeter was showing a constant 20-25 amp charge to the battery which was unusual and the voltage was 27.8V which was normal. When I turned off the AC in cruise the ammeter indicated zero, but as soon as the AC went back on I got the 20-25 charge indication. The airplane started normally twice that day. On Sunday when I went to fly my daughter's family home, the battery was dead. The grand kids swore they had not touched the switch for the aft cabin light which is on the hot bus. I thought of getting an APU to start but remembered there is a note in the AFM to not attempt takeoff with a DEAD BATTERY BECAUSE THE ALTERNATORS NEED A MIN OF 3V TO EXCITE THE FIELD. I suspect that I have a bad battery since the plane often goes 2-3 weeks between flights. I'm getting a new battery tomorrow, but I don't know what to make of the ammeter's behavior. Any educated thoughts on the matter would be greatly appreciated.