My personal theory is that he didn't lose or transfuse enough blood in the hospital to lose the power.

During that last push to the Louvre in the transport carrier, our boy Cage is still pulling off too many amazing 360 no scope one shot behind the back kills for me to believe that he hasn't done this stretch of the mission a few thousand times. I think the difference is that he's figured out his fellow soldiers will perform much better if they think he's lost it and this is there 1 last shot at victory, no take-backs, no 2nd chances, permadeath.