If you go to BryantRV.com you should be able to find a manual with troubleshooting. That said:
1. "Standing Pilot" model?
2. If so, is the Thermocouple well placed in the Pilot Flame?
3. We had one, happened to be an Atwood, but the wind could blow the pilot out, and also when the main burner cycled out, it did so with a POP! and that often blew the pilot out.
4. Make sure everything is clean including the big "Burner Tube". That there are no nests and debris in it.
5. There's a device called "Re-Ignitor" that's supposed to address this. I think the way it works is that if it senses (and I'm not sure how it does that) but the Thermocouple hasn't cooled off and turned the pilot gas supply off, it Sparks and should get the pilot lit again. That would cure the problem of Pilot being Blown Out by Main Burner Shut Down.