I tried an experiment on Friday before leaving for the weekend and I just came in this morning to find that NX is still up and running. The experiment was to run a program called Amphetamine, which prevents your Mac from going to sleep, and it appears to have worked. So it turns out the problem was with the Mac going to sleep and that somehow those settings were changed/reset when I upgraded OS X. Anyway, I’m back up and running.
That being said, I think it’s worth alerting the user when installing NX that this is an issue and to either instruct the user to alter the preferences or have the installer do it for him/her.