I have a precision temp r500 instant hot water heater for my RV. When I turn on a hot water tap the igniter comes on for 5 seconds and lights the flame, as soon as the igniter goes out, the flame goes out. The cycle then repeats itself. I checked the spark lead and the ground lead, and both seem okay. The LP gas is full. The green light is on. Any suggestion.

Hi and welcome to FixYa, I am Kelly.
Here is the Service Manual:
http://www.precisiontemp.com/Manuals/RV500_Service_Manual.pdf

Before you troubleshoot inside the unit do the steps in para 3.3 page 7 of the manual to make sure you have good power.

There is a testing procedure on page 39 that should cover everything stated below.

Do the flow-meter check para 4.2 page 12.

Do the thermistor tests para 4.5 page 12. (See figure 5 page 18 for resitance readings)

Page 19 will show you test points on the control board.

DO NOT do the auto-calibration procedure para 4-15 page 38 until you know you have corrected the problem.

This should help you resolve the problem.
From here I think this is related to the flow-meter as you have no other failures. If there is debris in the flow-meter assembly and it stops turning / measuring flow rate due to debris; you will have the symptom you describe.

Thanks for choosing FixYa,
Kelly