Your question confuses me. You said it won’t stay it, but then you ask if it could be the ignitor -which is the part that lights it.
SO…it lights? Doesn’t really matter I guess, since the ignitor and flame sensor are parts of the same part. The wiring to that assembly is just as important…as is the quality of the burner flame impinging upon the flame sensor. SO…
Make sure the electrical connections to each electrode are clean, corrosion-free and tight. This includes GROUND.
Make sure it has a strong and good quality flame.
Honestly, you’ve really not provided near enough information. Additionally, perhaps you can share when it was made. There were some changes to those tilt skillets some years back and that detail might be essential for accurately troubleshooting it. The date it was manufactured is embedded within the unit’s serial number. Here’s an photocopy “excerpt” on how to determine that. This info is from an old Cleveland manual (that’s not your equipment), but conveys how Cleveland does their serial numbers:
For some clarity in your troubleshooting endeavor, here’s some of my notes on that tilt skillet that might be helpful:
CONFIGURATION: Has just a main burner. No pilot system. Conventional setup for DIRECT SPARK IGNITION. Has SEPARATE ignitor and flame sensing electrodes on a common base.
NORMAL FUNCTION: Upon a call for heat from the thermostat, the module energizes (24v). It trials for ignition (4 seconds) and proves MAIN BURNER flame. When call for heat stops or the pan is tilted up, all power is removed from module.
MODULE SAFETIES & INDICATIONS: Module does up to 3 trials, with a 30 second inter-purge between each. If 0.7μA of flame current isn’t maintained, lockout occurs following the 3 trials. An LED on the module flashes, but the Benni Technologies data sheet for this module is extremely vague about how to interpret it.
NOTE:The OEM part number (KE603774-1) for the Benni Technologies module isn’t in ANY of Cleveland’s parts manuals. It appears to be a replacement part that’s never been formally published. Incidentally, this skillet’s models manufactured after Aug 2011 are using a Fenwal module (p/n KE603774-2).
CONTROL PANEL INDICATIONS: There’s no direct indication of a lockout condition. However, observe the AMBER heat indicator light for clues since it’s connected in parallel with the MAIN VALVE. The light will illuminate during a trial period and subsequent heat cycle. If the light short-cycles up to three times with a 30 second interval between each, that’s a hint to an ignition problem.
TESTING FLAME CURRENT: Connect a micro-ammeter in series with the flame sensor’s wire. Minimum reading is 0.7μA.