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That is a pretty old unit.........but, there should be parts available still. Some testing would need to be done to find out what parts it needs. Sounds like maybe a thermocouple and a heating element. I am attaching a link to the Dometic Service Manual which covers this unit. Print out a copy as there is some good information in there. I just repaired an RM53 this week in my shop and it is working great! Let me know if you need help with the testing. Don't forget to have the LP pressure checked at the tank regulator as that can affect the LP side. If the pressure is too low the thermocouple may not get hot enough to keep the gas valve open. Hope this proves helpful here. Please get back to me if we need to dig deeper into this as all follow ups are included in our fee. http://bryantrv.com/docs2/docs/RM77.pdf
Just checking back in to see if you might have missed my earlier response to your question? If not, please let me know if you need more input from me here.