Why does my Power Miser Water Heater keep turning off?

Not sure what screen you refer to, but the simple fix, assuming you have done all the correct pilot re-light procedure's, the cheapest part to try is a Thermocouple, easy enough to try it DIY.

Get more fresh air to the unit.
Clean the air intake/ flame trap/ flame arrestor located on bottom of tank.
http://waterheatertimer.org/images/Flame-trap-inspection-325.jpg

Post question on pro water heater forum.
http://www.thetankatwaterheaterrescue.com/forums/forum3/

Add a comment with type of gas control valve, for possible troubleshoot.
Copy following link to read service manual by type of gas control valve:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

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

Make sure thermocouple tip is seated inside the burner flame.
Make sure thermocouple is not overtightened. Finger-tight + 1/4 turn.
If the pilot lights, then ECO energy cut off is not tripped, but gas control valve might be bad.
Check color of pilot flame: it should be strong and clear blue.
If pilot flame is weak, or color of flame is yellow-orange: Clean pilot orifice and burner and combustion parts on yearly basis.
Clean air intake screen if applicable.
Increase air supply to water heater. Open a window and see what happens.
Check for adequate draft going up chimney using match under vent hood to see if smoke drafts immediately upwards.
Bleed air out of gas line.
Check gas pressure.

Open following links for troubleshoot resources:
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf
http://waterheatertimer.org/pdf/Pilot-outage-troubleshooting.pdf
http://waterheatertimer.org/pdf/Vent-spillage-test-atmospheric-gas-water-heater.pdf
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

More than likely the thermal couple is defective. The thermal couple is a safety device that shuts the gas off if the pilot goes out. If it is defective the pilot light will not stay lit. The thermal couple is the device that the small copper line goes to. It is mounted beside the pilot flame and the flame much touch the TC for it to work. If the flame is not touching the TC bend it until it is in the flame. If it is touching the TC then replace it.

check and or replace the thermal coupling. the coupling goes into the main gas control, if the coupling is bad it will shut off gas supply. as a safety measure.

you mean it is only staying on for 35 minutes, if this is the case, then readjust or replace thermal coupling, if bad it will not sense the flame or pilot light. it has to be in pilot light flame as to work properly. ( this is for a gas hot water heater). if bad it will shut gas off to heater.

IF its balance flue it could be blocked . Burner or orifice blocked lack of air to pilot slightly blocked thermocouple defective .

replace the thermo

change the gas valve, if the thermocoupling works and the piliot stays lit then it has to be the gas valve check to make sure the screen is clear also,, you said it's propane, check to make sure it is all the way turned on, and has the right pressure it might have a bad regulator on it, but will let other things in the house run good luck

I have the same problem. Water heater operates on a very simple principle. of thermo-mechanical feed-back and response. In my case, I have a Kenmore Power Miser 6, NG heater with an electronic pilot ignition system. The heater is just over one year old and last month (conveniently just after the 12 month service warranty expired) the pilot light started extinguishing on a very regular basis. I find it interesting that the very problem I am experiencing, is happening to other Kenmore owners (victims). The solution can be found in replacing one of two possible components; the pilot assembly or the gas valve manifold. The price of DIY pilot assembly replacement is approx. $60 . The valve component is significantly higher. Water heaters are designed and built to provide years of trouble-free reliable service. This is the first Kenmore product I have owned. From a customer perspective, with regard to product performance, Sears/Kenmore needs to take a strong look at their supplier quality. Oh, by the way, contacting Sears for remedial relief only managed to frustrate and infuriate me. You see, I am in Quality for a world-class aircraft company. I understand what ethical steps are required to satisfy a valued customer. I plan on ripping out the defective unit this weekend and replacing it with a reliable Home depot special. At least with HD, if the heater fails to perform , I can return it. Hey Sears in Chicago, don't come crying to the consumer when you are looking for the trendy "bail out". Signed- "Burned Out" in La Habra, California.