Verdict is in.. bad cell in battery. Went home at lunch and checked with multi-meter, it was reading 12.2v while connected to camper. I pulled it off and the battery was only reading 10v. So, the charger was pushing 12.2v which is acceptable.
I checked the battery when I took it out of winter storage and the water levels were fine. The battery shop I went to said 3 years is typical for a travel trailer battery. Perhaps the previous owner ran it dry at one point but it was working fine last fall.
Oh well, new battery installed and I'll take good care of it.
My power center / charger is a WFCO WF-8955-PEC.