Propane cooktop burners - one goes out frequently when first lit, worse in cold weather

I have a GE PGP966SETSS cooktop with a propane conversion kit applied. For quite some time, the front left burner has some odd behavior. When you light it, the flame sometimes goes out only a short time later and you need to relight it. Once it has been on for a few minutes, at that point it will stay out at not go out again. This seems to be more common when it is cold out, and rarely happens over the summer, but once the temps drop it happens more frequently. Additionally, sometimes...

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via Propane cooktop burners - one goes out frequently when first lit, worse in cold weather
by BlueWRXPride