Why did you disassemble and clean it in the first place? Were you having issues with it before? Definitely may be faulty and time to replace it. You can also call your local dealer to see if your MINI qualifies for the extended warranty on the P/S pumps. Check your P/S fan too to make sure that it's not seized/faulty.
Rebuilt units here:
Mini Cooper & Cooper S (R50/R52/R53) - Steering System - Page 1