Can you post the model/make of your fridge? We assume it is a Dometic but not sure it if was changed put along the way.
From your description it sounds like you have a model with auto ignition. Sometimes the igniter module does go bad. They should snap hard about once a second from when they start sparking and you can hear it outside next to the fridge panel if you listen. If is misses several strikes in that once a second pattern and is not consistent, this points to a problem. They should spark non stop for a good amount of time until it times out on safety and shuts down. I cannot recall the time period but it is about 30 to 45 seconds I think on the first, second and third try. And on the newer units, it tries 3 times of a lighting sequence to ignite with a time delay of a gas purge in-between and then total shuts down on safety.
Have you pulled the little metal cover over boiler burner area where the igniter is? Is there a lot of rust and crud in there? and is there crud fused between the igniter electrodes?
Also, if you light it with a match or grill lighter, once lit will it relight later?
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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