Had a similar problem with my '05 Safari Simba with the 5500 Onan. Would run for awhile then stop....30 mins or so off and would restart again. I didn't think about it until we got back from a trip....the shut off coincided with either climbing or descending a long grade. I had a low oil level. Not a lot but apparently enough to trip the low oil sensor and shut it off. Filled the oil back to full and not a problem since.
Used to tow a 2008 Wrangler. I found a posting that suggested pulling the "IOD fuse" & "M1 brake fuse". Had an earlier model 2008 that needed the key in the ignition to unlock the steering. Pulled that Wrangler over 11,000 miles driving between 5 - 8 hrs a day. Used a Brake Buddy powered through the accessory hot point. Never had a battery problem. Here is a link