The battery serves as a capacitor for smoothing the power from your converter. It also supplies power to the emergency break-away brake system, when needed.
Typically, travel trailers have parasitic loads even when in storage. Circuit boards, alarms, and radio memory are usually powered and can drain an RV single battery within a week or so. If you wish to leave the battery on the trailer, disconnect one of the battery terminal wires. The existing charge in a fully charged battery will still have a fair amount of charge left within a month (if disconnected from trailer electronics).