Well, I don't like your example because in order to get a clearance to handle secrets it is typically voluntary insomuch as we have an all-volunteer military. As we are, generally speaking, allowed to sign away rights I simply don't think this is a free speech issue.
Ok, how about this: you may not legally publish anything that is dishonestly defamatory or that maliciously or damagingly misrepresents a person. Even though you have free speech, that act harms your fellow citizen in a dishonest fashion, and is justifiably illegal and therefore justifiably a limitation on your right to free speech.
Similarly, let's say you repeatedly use a firearm in a way that threatens others for the purposes of taking things from others in a fashion that is harmful or even violent against that person. It is my view that it is reasonable to have some amount of time that your right to keep and bear arms may reasonably be restricted, even beyond any incarceration for conviction of the original crimes.