This is a pretty long-standing problem. The only known way to get around it is to delete your test character and create a new one. Then you should be good till the next time it happens.
I just saw it in the list of known issues. My bad for not checking there before posting. I did find that the problem went away after a couple of hours, so I had chalked it up to the server being overtaxed.
Comments
See: http://forums.startrekonline.com/showthread.php?t=191605
EB
Having small kids helps. You can't stay stuck on one problem for any length of time.
EB