On my rca colortrak stereo monitor tv model# fpr725er the channel will not stay assigned to channel 3. The set spontaneously goes to black then after a few minutes will return to the station or the set will auto-scroll through all the channels and will not return to any channel. The problem appears to be related to the remote control within the set itself and not the controller

The channel frequency is supposed to be stabilized by the AFC system from the tuner. In your case it appears that this system has died and the processor is trying to compensate whatever it can.
You will need to open the tv and test the tuner for the AFC signal presence at pin 7 or 8, depending on the exact model of your tuner. If the around 7 volts signal is present then the tuner is defective, if it's not present then the processor has failed - just replace the failed component.
If it's the processor then it's the entire jungle circuit that will have to be replaced (the one with 48 pins) - this is a job only a very experienced repairman can do, you will have to call one.

Good day!!!

Please try to reset auto scan on your TV...

just go to the menu and find the auto scam mode..

complete the 100% scan for better results..

If the problem persist just add a comment to give you a more possible trouble shooting...

I need to hear any feedback from you to go for further troubleshooting...