One of my showers has started to malfunction as of late. I have great pressure when tub is filling and when shower is engaged. (Initially) After the shower runs for a minute or so, the pressure from shower head drops dramatically. You can hear the water pressure change by the noise it makes.

The knob that switched from tub to shower is intact, not moving, etc... I am confused.

You sure this is not the tub/shower knob? When shower head starts to have pressure drop can you switch to the tub and watch full power from the tub faucet? After confirm, then switch back to shower and is it strong again for a short duration, or still weak?

Could also be something lodged in the pipe? You could remove the aerorator from your shower head (clean it) and leave it off. Run your shower for 5 minutes full blast to clear out any crap.

Try that and get back to us,
Knucklez