I had the same symptoms until I didn't; that is it simply quit all-together.
Years ago I replaced the Blower Motor Regulator and that worked for about 4 years. Today, there is no fan (again, it was erratic for a while, then it stopped).

Moving forward,
1. I am a good w/electronics and solder, so I did the repair you suggested replacing the 47K rheostat with new. - no improvement.
2. I installed a second new Blower Motor Regulator, at the fan. No Improvement. The unit was very warm when I removed it after only a few minutes testing.
3. I removed the new Regulator and also the fan, did a 12VDC bench test on the fan motor and it ran well, nice a smooth.
4. I tested the readings on both regulators, the old one did not match the new one, but there were no dead shorts.
5. Lastly I tested the pins (Car Side) at the Regulator, found good steady voltage on RED/BLK and variable voltage on center pins when rotating the fan speed ****...

I am clueless on why this thing will not run.
Any thoughts?