I'm going to go with the others that suspect you have "phantom" loads you don't know about that are draining your battery
However, a questionable battery
from Walmart isn't unheard of. Also, I believe they use the term "deep cycle" a little loosely, often referring to hybrid starting/deep cycle batteries. If the battery
specs refer only to CCA (cold cranking amps) you probably don't have a true deep cycle and as many amp-hours as you might think.
I don't have much use for the plug in volt meters. However, if the trailer is plugged in and the meter reads in the range that Jon provided you then the converter is charging the battery.
If the trailer is not plugged in, the converter will not do anything. Just a lump of wiring.
If your inclined to buy tools at the slightest need (as I am) then a clamp-on digital ammeter that reads DC amps (not all do, check the specs) then you can clamp around one of the battery wires while the trailer is "resting" and it'll provide the total "phantom" amp load.
Sources of phantom loads:
Refrig control board
Digital clock/alarm or TVs running on 12vDC. Even TV's turned off have a draw.
Volt meters (like the ones stuck into an accessory socket
Assorted stray current, usally from improper grounds. (this is a real problem with fiberglass boats)
The best defense against any of these a battery switch in the positive battery cable. Needs to be pretty heavy duty.