RV Repair: Hot Water Heater, flame ionization, hot water heater

Question
After I light my Hot Water Heater with the Water heater on switch it will heat the water but then as it cools will not come back on automatically to keep the water warm.

Answer
Sounds to me like you have a DSI water heater (probably an Atwood). There are several common problems that cause this anomaly - assuming that it does attempt to re-light itself(valve opens, igniter sparks). When a DSI water heater lights, the electronic board completes several tasks:
It opens the gas valve and begins to spark (simultaneously). When the flame ignites, a process called "flame ionization" allows the flame to act as a "wire" and complete a circuit back to the water heater, telling it that it is lit, to keep the valve open and turn off the igniter. The same probe that created the spark at the end of the burner tube is used to sense the flame (New models only use one wire, early models used 2).
The most likely problem is in the positioning of this probe.  It may be placed well to ignite the flame, but if the flame is not making contact between the spark probe tip and the ground probe (or sense & ground probe on 2 wire models), it will not tell the board that it is lit, therefore closing the valve and turning itself off. Adjust by bending the metal bracket (not the probe) with pliers.
other items to check:
Good grounding through the screws holding everything together - loosen and re-tighten.
Check the wires & connections - check for breaks and clean connections with a wire brush or steel wool - Do not touch the spark probe or wires with power on!!! (600,000 Volts Hurts!)
The gap between the 2 probe tips should be 3/16".
If the W.H. does not even try to spark, the problem is likely in the board or connections. Remove the wire harness and clean the contacts on the board with a pencil eraser. Check ground screws. If this doesn't work, have a service center test the board.
The final possibility is the T-stat or e.c.o. These 2 work in conjunction to ensure that the water does not overheat. Both act as switches and if 1 of the 2 is stuck in the "open" position, it will keep it from lighting. These can be checked for continuity or voltage.
As far as what causes intermittent operation after the waterheater has cycled, my guess is it's simply the contraction and flexing of metals as they are heated.