First try taking the safety cut-out (looks like a diode in a plastic sleeve) out of the circuit by disconnecting both ends, one from thermostat, and other incoming power wire end, then just connect the female incoming spade connector directly to terminal on thermostat where it came off. If that fixes it, replace the cut-out.( thing in the plastic sleeve) If that doesn't fix it, try cleaning electrode ends well and retry, if no luck, replace the electrode assy. The electrode is also the flame sensor.

I had that same problem and that solution with the plastic diode worked. can i still run the hot water heater without that thing in there? What exactly does it do and how does it work?