It would be better to determine the cause of the battery
going dead rather than just buying a more expensive battery
that would also go dead if the power drain is not discovered. AGM batteries require different charging than flooded lead-acid batteries, so check your converter to make sure it is compatible with AGM. Regular old deep cycle batteries can last many years as long as they are not drained down too much, most recommend draining to no less than a 50% charge.
I have at least 3 items that place a drain on my battery
when not in use (gas detector, radio memory, and electric brake circuit checker), but I also permanently mounted a 90 watt solar panel
on top that keeps it topped up daily.
A cutoff switch is also a great idea for long term storage if you have items trying to draw power, and Larry Gamble has kits available for that at Little House Customs