I have seen a few different versions of this, more regularly in modeling than drafting. The first thing to do is to run part cleanup. File>Utilities>Part Cleanup and it probably won't hurt to turn on all of the options. If it fails to run part cleanup some of the options may work but not others, and it would be instructive to know which ones failed. Feature data structures do tend to be the culprit when this happens.
If there is a model involved rather than just drafting then the highest represented class of problems that we have encountered stem from wave linked geometry. These problems are by no means frequent, but sometimes finding a solution is quite involved and tiresome.
Another possible cause may simply be that you don't have write access to your files. Try again after moving or copying the files that you're working with to the local hard disk. Not MyDocuments or the desktop, especially if you're on a company network with roaming profiles. Networking can be done lots of ways and could complicate things. Best to take out all the variables when you need to solve a problem.
You also probably want to get right out of NX and open just one file at a time. Again this may be just about narrowing down the causes by eliminating variables. Sometimes errors withing NX are related to memory management isuues, although your error indicates a symptom of a problem that has occurred earlier and left a bad taste behind. Have a look at the other applications that you may be running on the system and turn off anything you don't really need at least until the problem passes.
Good Luck
Hudson