^But isn't this where if they had been more serialised, they could have avoided such issues. In an episode inbetween "Message in a Bottle" and "Living Witness" you have a line of dialouge that you've been able to construct a back-up module for the EMH?
Now as for being unable to create another one, they seemed to have no problem with repairing hull plates, interior bulkheads, building not 1 but 2 delta flyers, repairs to shuttlecrafts etc.. So it's seems unlikely they wouldn't have been able to build another back-up module for the EMH after the first was lost.
It's not the audiances fault if they call the writers/producers on it for being inconsistant. The drew attention to the fact that they didn't have a back-up module for the EMH, if you want to have one good writing would say you inform the audiance before you plan to use it you now have one.