There are several issues possible.. For one: What converter do you have. Some are better than others at making a battery last and last, Some are not good at all, And how long do you leave it unplugged between trips.. As others have said parasitic draws will take a battery down in a relative short time, Lifting the negative cable or a battery cut off switch can help here big time.
Next: If the battery is not a maintenance free design, when was the last time you checked the fluid level? The fluid is a dilute acid and you may need to add DISTILLED WATER, the level should be between the top of the plates and 1/8 inch from the bottom of the filler tube (Leave a 1/8 inch gap).
Finally there is the size of the battery itself.. A common battery in small trailers is a group 24, about 75 amp hours, Marine Deep cycle you can safely use only around 20 of those amp hours before serious battery damage happens.
I just dropped (Well lifted) a pair of Gold car batteries into my house battery pair. 230 amp hours. I can safely use 115 of them before serious damage happens. Clearly it takes .... a bit longer... to run these puppies down. That is over 3 times the Group 24, it is about half my total battery capacity and being true DEEP CYCLE I can use more of it. (Soon as I replace a fuse I popped today or Thursday).
The six volt golf car battery, used in pairs, in series, so that you end up with one 12 volt (bat)T(ery) (Bat is six volts. T is a jumper and ery is another six volts making one 12 volt battery) are so popular because golf courses order them by the pallet load for their golf cars. making them less expensive overall.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times