40,000 BTU, 50 gallon tank, Model PR650NBRT, Serial # H01106592. Pilot light not burning. Turned off gas control knob, waited per instructions, turned to pilot position depressed knob
Lit pilot, held knob depressed about 1.5 minutes, released pilot did not remain lit. Repeated steps again pilot still failed to remain lit. The control knob pops up after releasing. Is this a thermocouple problem?

I believe it is the thermocouple. Should be relatively easy to replace. Cost would be somewhere around $25 or so (if you do it yourself).

Here is a helpful video.

Best of luck,
WallyH

Wally is correct the problem was the thermocouple. I paid $4.33 for a new thermocouple installed it myself in about 15 minutes and I can have a hot shower again. Thanks Wally for your help.

You need a new thermocouple. DrTom4444

My issue looks little different. After pilot ignition, the flame stays for no problem, then I truned gas from ignition to 'ON', then set temp to high, the big burner started to fire, but after abot 1 or 2 minutes, suddenly the big burner flame is gone. I watched a few times, when the big fire is gone, the ignition head is red, so I am puzzled my situation...

Where did you buy the thermocouple? We have the same problem for the same model number water heater.

It sounds like the flame is hitting the tip of thermocouple different once burner comes on. It should hit the tip and cover about 1/4" on tip, any more and it will quit working. You always have to adjust a new thermocouple to get it right. Watch the pilot when the main burner fires and see what happens. Check to make sure all shields are in place, too. A shield not put in correctly will let air come in and move the pilot flame stopping the gas valve.