I've thought about this, and there are two things to consider.
Ever heard of the philosophical problem where you fix rotten pieces of wood on a sailing ship by replacing them with fresh pieces - until you've replaced every piece? The question goes - is it the same ship still? I would argue that you really do have the same ship still. Because the pattern was the same at every minor wood-replacing step, you always had the original ship. This holds for brains (the wood of the ship) and minds (the pattern of the ship), because after all brain cells die and have to be replaced - and yet your mind is the same. So, what you have to do is transfer the mind bit by bit, while maintaining functionality - you have to transfer the mind without introducing a discontinuity in its existence. While this would make the whole process hellishly difficult, there is no reason inherently that says it can't work that I am aware of.
(incidentally, the philosophy problem continues by saying - what if you reassemble the original bits of wood into another ship. Is this the original ship too? Do you have two then? I would say that despite being made of the original materials, the discontinuity in its existence makes *this* the copy)
The other thing to consider is whether or not this is happening already anyway. If you fall asleep or get knocked unconscious, your consciousness is interrupted - and when it gets recreated, is it the same one or a new one? Is your consciousness now the same consciousness as you had a second ago? As the pattern is identical, you cannot tell. if you were copied into the computer, the computer-based version of you wouldn't be able to tell it was inhabiting a different mind, for it the process would be continuous.
Your signature is oddly apt, considering ;)