Somebody at StarFleet HQ is stealing ships! One component at a time, they collect the parts needed till they have a complete ship then they sell it, and it is up to YOU to stop them!
hmmm ... not a bad idea, BUT as was mentioned, stealing a ship one piece at a time would be way to time intensive.
It would work much better if someone was stealing certain systems one piece at a time instead of a whole ship. For example, stealing Starfleet sensors or ship computer systems would be more logical, harder to catch, and still present a MAJOR breach in Starfleet security. If enemies can get hold of working versions of your top-of-the-line electronics like that they could easily find the weaknesses in these systems allowing them to come up with ways to hack, confuse or disable them putting the entire fleet in serious jeopardy.