I took the batteries to Canadian Tire and had them both tested. Apparently both are bad!
Lousy luck? Or is it possible that my trailer is doing something to the batteries to kill them so quickly?
JLeising - As soon as I get a new battery, I will test the amps while charging.
JohnVtx. I will take a pic of the wires coming from the battery. I don't see anywhere where anything could be tripped. Maybe I am missing something.
5picker - I tested at the converter and got 13.56V. I tested on the battery terminals with the battery connected and got 13.56V. I disconnected the battery, immediately checked at the battery terminals again and got 11.96V. 45 minutes later it was at 10.96V and had been disconnected for that whole time.
ShermanD - It's a deep cycle marine/rv battery.
And this "he" is a she!
Thanks for all your help everyone. I will replace the battery (got it at Costco so shouldn't be a problem). I have a hard time believing I got 2 bad batteries in a row though so still think something must be going on. I also wonder why my converter never seems to go into bulk charging mode.
I will keep this post updated.