Your water heater using the SAME circuits/t-stat-ECO & thermal-fuse for electric and propane so if electric is working (heating/shutting down/reheating) then problem is NOT with any of the above.
Problem is with spark electrode, gas valve solenoids and/or burner assembly
Firing off, running for few seconds then making attempts to light off should have triggered 'lockout' and RED Fault light at On/Off panel.
That indicates spark electrode issue:
*dirty...carbon/soot build up....clean with emery cloth
*not being engulfed in main flame...tip red (needs to be in main flame to generate 'proving' signal to circuit board----no signal/circuit board shuts it down)
*incorrect spark gap.....S/B 1/8"
*burner tube not properly aligned.....gas MUST flow directly down center of burner tube in order to properly mix with air for proper combustion. If burner tube not aligned the propane will bounce down side walls of tube , not mix with air and not light off/stay lit
*flame spreader on end of burner tube not 'squared' (parallel) with end of tube...propane doesn't properly flare out and ignite/stay lit
*main orifice dirty.....unscrew from gas valve, soak in alcohol, blow out with air (no poking anything thru it)
Gas valve solenoids get 12V DC poser at same time spark electrode gets power,
You can FEEL them energize (only for 6-8 seconds unless main flame proves)
Make sure connections/terminals are clean/tight (RED--power/Black--Ground)
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31