It bugged me no end when they made such a deal about 'sending' the Doctor to Jupiter Station or anywhere else. Why would they have to delete the software to send a copy of the program anywhere? Was the thing made by Microsoft or something?
If the Doctor's consciousness was based on quantum-computing principles, a case could be made that it couldn't be copied, since transmitting quantum states (as in quantum "teleportation") requires destroying/erasing the original states, otherwise it's a violation of quantum conservation laws.
That wouldn't explain the backup EMH in "Living Witness," though. But since Voyager never managed to create another after losing that one, perhaps there was something unique about the process whereby it was created.
I believe the back-up EMH is :-
A continuty error that they hoped wouldn't be picked on.
It was just another in the long list of things that the producers hoped the fans wouldn't pick on. It was however still a good episode.