If it has the little thermal cut-off in power wire to thermostat (has a little plastic jacket over it) try removing it, and connect female spade from power wire, directly to male spade on thermostat, and see what happens. Also, make sure electrode is positioned in flame good for flame sensing properly.
Make sure propane is on and getting to your stove burners ok, first, then try switching it back on. If it fails to ignite, shut switch off and try a couple of times, if still no ignition, get back to me.
If this model has a thremo couple you might want to check it. It sounds like that is the problem.
Normal causes for that would be by-pass valve not in proper position, or defective, allowing cold to mix with hot, or thermostat not touching up against tank properly, or defective. Do you know where that thermostat is?
Look where the black foam cover is, with white letters, below pressure relief valve. One is lettered ECO, other THERM. If you note where the wires go, so as not to mix them up , and pull them off, then peel back the foam cover, you'll see 2 little round discs, that are held against the tank by a small spring. They need to be checked that they are in there properly and are up against the aluminum tank.
The thermocouple sensor may not be in the best position to sense that the pilot is lit.
Adjust the thermocouple mount or simply bend the thermocouple "wire" so that the pilot flame is touching the tip.
Mine is pretty new about a 1year in halve to two years old. i light with lighter it lights burns great then acts like propane cutts out then burns low then cuts out kinda acts like propane pressure cuts out in the valve but i can relight 30seconds later same thing. i have checked stove it burns great. is it in the waterheater propane valve. need help pease i need a cheap fix layed off right now. thank you dave