Oven on Suburban model SRNA3 will not stay lit!

Just did another test. Pilot lights fine. Then burner lights fine. Then at the 4 minute mark, the pilot goes wonky and starts puffing on and off, then finally shuts off which in turn shuts off the burner.

You can actually hear the pilot when it's puffing on and off like it's starving for gas, then it goes totally off.