If you use MSI Afterburner and adjust the fan manually, does it change? If it doesn't, it's most likely a faulty fan controller and the card needs to be RMAd.
The fan only responds on the 87% to 100% speed range. Below that it doesn't spin.
Edit: Figured it out. The fan is broken. (even though it's able to spin at full speed)
I have two HD7850, i switched the fans.
Card with problem + another fan = All Good.
Card without problems + my fan = Problem appears.
So it's time for shopping. For future reference the fan you need to buy for an HD7850 it's a model: FD7015H12s (12v 0.43a) it costs $10-$15 and takes about 10 minutes to replace.