Yes, there are a few things.
First, did a little red light turn on inside on the tank level monitor? It would have the DSI letters next to it, meaning an ignition fault.
But you said this,
Pretty straight forward since the new one was exactly the same as the old one except for electronic ignition.
Not sure of your camper model year, but the T264SR model started in 2004 so you would of had a newer Atwood heater with DSI. (Direct spark ignition). The 2004's to 2007's were the same. Unless you have a very early 2004 build date in 2003 which might have the older pre 2003 redesign. But the gas system worked the same on the prior 2003's just the 120 volt electric element part was different.
What was different in the new heater versus the one you took out? Got pics?
For the gas burner and ignition to shut down before the heater reached 140F sort of points to this if it was not a DSI fault.
1. Some how the unit lost 12 VDC power to it. Loose wire maybe?
Odds are low, but not impossible.
2. The new T stat or the ECO thermal disk switch is tripping too early. If either of those switches open up early, it will shut down the heater and you not get a fault. Then when it cools, it may reset and work again until it gets to that heat that is causing a false temp rise.
3. A connection to the PC board is loose, heat may change the connection.
4. The PC board has issues affected by heat. Hopefully not this, but it is not impossible.
The above "assumes" you are running on LP gas only. And not electric and gas at the same time. If the heater was on electric, heated up the heater, then you flipped to gas, 5 minutes may be long enough to heat the rest by gas.
A cold heater, water is 50 to 60F from the well or house, it should take a good 35 to 45 minute burn by the gas only to come up to temp. If the tank was hot to setpoint, then cooled over night, a gas reheat could take approx. 20 minutes.
You can check the water temp, but running hot water out a faucet after purging some water with a thermometer in the water stream. The heater is supposed to shut down at 140F. What water temp does yours's shut down at?
If none of the above seems to help, do you have a volt meter and know how to use it? We can help with trouble shooting further if needed. Please post a pic of the outside of your new one. Dometic may have changed something since the last Atwood's where made.
Hope this helps