You have a flame sensor located within the same area as the ignitor, probably on the other end of the burners.(it looks like a short metal rod and is held in by a 1/4 inch screw and has one wire attached to it) If you clean it, using a piece of plumbers sandpaper or steel wool, this might correct your problem. These sensors get dirty from time to time and if they don't since the flame they will shut off the gas. That's the reason for them.
However, if this does not fix the problem, I would be looking at replacing the circuit board. It's a costly item, but everything goes through it and its your only part left to replace. Hope this helps.