Atwood 7916 intermittent lighting

I would start by cleaning, checking burner, electrodes and orifice.

Dirty furnace! Blow it out good with compressor or canned air. Locate your sail switch and blow that area out good.

RV furnaces try 3 times to "prove" the flame. Yours having trouble proving and measuring the flame. There is a flame rod in the flame that conducts a very small DC current as long as the flame is established. As quickly as that signal is no longer present, the sensors on the control board kill power to the gas valve and safety off to prevent unburned gas from collecting which could cause an explosion. Your furnace is doing exactly what it's supposed to be doing. You need to figure out why or hire someone knowledgeable to fix it.

My older 8531 did that. It turned out the "burner" (you have to unscrew a few things to get at it back in there--see a youtube) --use a magnetic screwdriver or go insane--was the culprit. It is tongue-shaped sticking out the back, with a screen on top of the tongue above where the flame comes out, and below the sparker set.

My screen (supposed to have a bunch of little holes in it) was rusted badly and had a big opening instead of a screen for part of it. That made the flame come up unevenly instead of properly through an intact screen, so the flame sensor got confused I think.

You could get a similar effect from just needing cleaning as already mentioned. Also wasp nests. As they said above, take it all out and see if it is anything obvious. While it is all apart now is a good time to clean out the propane line to the burner and the orifice sprayer hole --not with a pin!--see the maintenance instructions and a you tube for that.