Richmond LP PowerVent water heater stops heating. LED's A&B, indicating it has cycled three times without ignition. Watching it go through its cycle, the heat plate glows, hear a click, no flame, shuts down, tries three times. Reset works occasionally, but seems to be only after it cools down?? Even when it works, it runs for about 5-*10 minutes, shuts down before reaching temperature, then immediately tries several times to fire up again, but usually fails after three attempts.

According to photos listed for that specific model... it is NOT power vent.
It is ordinary atmospheric gas water heater with 3" vent pipe
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Gene

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http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#pressure

3 flashes, failed pressure switch?
Test pressure switch
Gene

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Buy igniter at local plumbing supply house or call manufacturer as shown on label side of unit; might want to test the device:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#igniter
http://waterheatertimer.org/Water-heater-manufacturers.html
http://www.thetankatwaterheaterrescue.com/forums/forum3/
Gene
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1) Rheem-Richmond does not post service manuals:
Copy following link to identify service manual by type of gas control valve:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

2) For lockout, the air intake might be clogged or combustion parts dirty, causing overheating which will break TRD glass vial. Gas control may need to be replaced. Reset gas control by rotating knob to lowest temp for at least 6 seconds.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html

3) Call Rheem or local service tech.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

1) Could be the vapor sensor. That's a suspect.

2) General troubleshoot: clean burner and combustion parts, clean air intake, bleed air from gas line, check gas pressure. Color of gas flame should be clear blue, and flame should be strong, and no combustion by-product dripping back into combustion chamber. No chemicals of any kind stored in air supply. Plenty of fresh air. Water heater in hot attic needs more air. If water heater has igniter, then igniter has to be checked. Flame sensor must be positioned correctly and operational at time of combustion, or sensor will signal gas control to turn off gas. Gas control valve can be bad.
Open following link for possible illustrations and reading.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

3) Specific troubleshoot begins with identifying gas control valve and reading the service manual.
I think the Rheem/Richmond power vent has intellivent gas control
Open following link to identify gas valve and download possible service manual:
http://waterheatertimer.org/How-to-adjust-water-heater-temperature.html#intelli

4) Take a moment and rate answer:
And take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Start-point is to inspect and clean burner parts and combustion chamber, clean air intake, bleed air out of gas line, test gas pressure, test electronic gas control valve, check for venting issues.
As general rule, gas water heater manuals recommend professional service once a year that would cover most items listed above.
To see images, and for more reading and resources, look at your product manual and open following link:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean

Richmond/Rheem sells power vent blower assembly that cost about $300.
Your product manual shows part numbers.
http://www.monstermarketplace.com/heating-supplies/rheem-sp12562-blower-assembly-powervent-2
Replacement gas control valve costs $300

http://www.digelair.net/pdfs/TECHLIT/BOSCH/MANUALS/Bosch-ProTankless_AM.pdf
http://www.bosch-climate.us/files/201009031238250.GWH715ES_English_12.2008.pdf

Above are the manuals required to diagnose and service your error code.

EA: No flame ionization detected with water flow.
Verify that all manual gas shut off valves are open. Check gas type. Reset error code and open a water tap to cycle the heater in an effort to purge air on new installations. Cycling hot water tap on and off multiple times may be necessary. If heater still faults with EA error code, have a licensed gas technician properly purge air out of the gas line leading to the water heater. Check three wire connections to ignition group on the lower front of the heat exchanger are secure. Check gas pressure. Check venting specifications are met. Improper venting may cause premature failure of the flame sensor rod. Check that the minimum power fan speed has been adjusted to the proper value. Observe inside the viewing window of the heat exchanger when a hot water tap is opened. Sparking should be followed by a steady blue flame. If flame is unstable or yellow with proper gas pressure.

Sounds like a bad thermocouple. This part sends a millivolt signal to keep the gas valve open but shuts it off when it cools - or if something goes wrong with the ignighter - to prevent fires. It's easy to replace and not super expensive. See your local Rheem dealer.

sounds like the circuit board is bad,, when you turn on the unit does the fan come on first if not you need a circuit board, depending on the age it might be cheaper to change the whole unit