With an overload on the 120v side, it can be a contest with inverters whether the "overload protection" (say a CB at the receptacle) pops first, or whether it pulls so many amps from battery/wiring on the DC side, it hits the low voltage shut-off. But there can also be a fuse on the DC side that can blow before the low voltage shut off, in an unusual situation as here.
A small wattage inverter in the 12v socket in the Winegard panel will have a glass fuse in its 12v plug that can blow. But also that socket is on the RV's 12v fuse panel with maybe a 10a fuse for the "TV circuit" Another contest which will blow first.
When you use the optional clamps wiring set that comes with the small inverter, there is no DC fuse when you clamp to the battery posts as invited. You would install a fuse when there is a ring terminals wire set being used.
I was earlier thinking it must have been an intermittent short in the 120v load (the 30/15 adapter) causing the issue, but now the OP has clarified what was the real problem.