Thanks to advice recieved on ausmini, I've had good success recently with gravity bleeding initially, then (if you can), letting the system rest for a day or so before bleeding normally. I like to have my assistant apply pedal pressure, to let the fluid that is draining drop the pedal to the floor. Close off the nipple before repeating (slow pedal operation like Mike said) on each of the other corners. After that (time permitting), you might like to repeat after a day or so. I think air bubbles work their way up through the master cylinder, or down to the calipers/wheel cylinders.
Another thing I was taught once was the idea of bleeding a new (read: dry) m/cyl on the workbench. Not sure how applicable it is to the simple mini system though.
One thing seems certain in all of this though - pumping the life out of it is no good for a master cylinder, and you are probably just creating teeny tiny bubbles which will never bleed out!
One other thing to mention is that an incorrectly built (or rebuilt) master cylinder can wreck everything. In my case, a ring in piston from some other assembly blocked the compensating port, so was never going to work properly.
Here's a pic - I forget which one was the correct one.
Good luck.