Shower starts v hot and powerful but gets colder quickly even though lots of hot water available
You probably just need to replace the cartridge inside the mixer valve.

Thermostatic mixer valves work by expanding and contracting from heat and cold, automatically adjusting the mixture to maintain the set temperature.

It sounds like yours is worn out, and as it heats up it is adding too much cold water, or not enough hot.  Turning it off for awhile lets it cool off a bit and start working normally again until it heats up.

Replacing the cartridge is a pretty simple job - turn off the water, unscrew the screw that holds the handle in place, unscrew the cartridge with a wrench.  The  take the cartridge with you to the store to find the exact right one.  It should come with instructions for aligning the valve and handle properly, so be sure to read them.