My comment on this matter is closely related to what McSnarf said about Voyager's EMH (The Doctor). This has been bothering me for years. In all the mindblowing advances in computer technology, they handle all their important data transfer via the cut-and-paste method. They have no copy!
In one episode of Voyager, the Doctor's program got corrupted by all the little "personality subroutines" that they had added. But, never fear, they had an EMH-diagnostic program that looked and talked exactly like him. So, what was their solution? They grafted the neural matrix of the diagnostic program onto the doctor, restoring his functionality, and in the process destroying their only EMH-diagnostic.
Now, did i miss something here? Why did they not just tell the computer to take the data that represented the "brain" of the diagnostic program, and copy it to another part of the computer? In the very least, i'd think they could at least replicate a copy of the storage medium that contained this information.
I also remember there being an episode of DS9 that had some problem that could have been solved much easier had they just made a COPY of some relevant data.
I don't think that technology was really lost between now and Star Trek. The technology is still intact. What we lost was our common sense. Look at Voyager for instance. This ship obviously has a COPY of the entire database of human knowlege, becuase the ship's computer has access to it even when they out of communications range with every other Federation computer in the galaxy. They can store the entirety of recorded human knowlege in an object the size of a human head (re: Data and his skull full of LED's), so there should be a small shoebox with a backup of their database stuck in a few random equipment lockers throughout every Federation ship. I assume these things could be mass-produced fairly cheaply based on the fact that Dr. Soong threw together a few of them in his basement lab. | 
