Our Lord Jesus Christ was the High Priest in His human nature. He prayed a lot, as any priest should. The healing is the divine power that comes in response to our prayers. Since His prayers were always true and perfect prayers, they were always fulfilled. Ours are not, because our motivations are not always true or pure, but selfish and ungrateful.
Well, I have to admit that I never thought of it that way before. So, are you saying that the Divine power within Jesus lay dormant during His physical life, but instead there was an exercise of power separately from the Father because of perfect prayer? I'm really stumped. :) I mean, scripture DOES say that perfect prayer gives perfect results. I have always thought that Jesus' Divine power DID manifest itself through miracles, by His own calling. You raise a very interesting issue.
Remember that the eternal God the Word humbled himself to become man. He came to undo what Adam did, to counter an undefiled man's disobedience with an undefiled Man's perfect obedience. His human will was never in conflict with His divine will; nor was His divine will in anything but perfect harmony with the will of the Father, and vice versa: for it was Christ who willed Himself to die with Father's concordance; and it was Christ's divine nature that resurrected the Body. So, I wouldn't say His divine nature was dormant; God never sleeps. :)