When deciding if your hired help is really giving the help you hired them for: Communicate first, demote second, and ban only if you have definite, historical cause for concern (not merely suspicion of bad behavior and hard feelings). Many questions arise from the inability to manage people effectively, and their responsibilities should be clearly spelled out from the get-go. Here's a look at some of the reasons why...
Communicate - Your staff are an extension of you, vital pieces in a working machine and a business structure. If you could (or would) do the whole thing yourself, then it's still not the best idea. Having at least one other person around who'll be honest with you--and not just blow smoke up your butt--about operational decisions is just a good thing, in general. You should be able to communicate with these people IN THE MOST DIRECT FASHION AVAILABLE. In case that wasn't clear: You should be physically capable of meeting them in person, speaking to them on the phone, or...in this age of global villagers--have multiple, regularly used IM screennames and emails for each of them. There is absolutely no excuse to have anything less. If any member of your staff is not available to you within a reasonable time frame, when an issue arises, then this person is damnably close to useless. There is no such thing as enjoying the perks of staff-dom without responsibility and accountability.

Demote - As others across TAZ have suggested, you can always take away access and ability. These things are privileges that need to be earned, regularly and with the interests of the board before their own. If you pay your staff, then this can be an end unto itself. No work = no pay, to just about everybody, but you can't just yank that [or any] rug without warning unless things have gone seriously wrong. Many interpersonal concerns are commonly avoided by setting up a clear description of duties beforehand. This is not to say that there won't be problems...there are ALWAYS problems...but what constitutes a "demotable" issue and what does not should be made understood, and most of these are not going to be gathered by osmosis or ESP.

Ban - Obviously, a choice of absolute last resort. You'd have to be pretty sure that such a person was going to (A) spam members with nasty "antiestablishment" whinings; (B) steal your members and start a new board (if they haven't already); (C) suddenly become way more active with a vendetta than he or she ever was in an official capacity; and/or (D) otherwise use their ACP privileges and passwords to damage your board. I wrote, nearly a year ago on TAZ, about how I had to have an hours-long IM convo with one of the founding admins of a forum I run, my finger over the "Ban button" the entire time. He was eventually encouraged to part ways of his own accord, but these sorts of conflagrations seldom defuse so constructively. If you don't know the people working for you, well enough to anticipate their needs and behaviors, then they probably shouldn't be working for you at all.​
Take, for instance, the incredible number of staff or staff-like positions on TAZ. It's patently obvious that certain individuals do a lot of the regular maintenance and heavy lifting. While regular members can't see who does a lot of the "behind the scenes" stuff, the other staff definitely can, and so can the admin(s)/owner(s) of any given board. What it really boils down to is what you expect from your staff and how well you make them aware of these expectations. If it's OK for them to do nothing more than check in once every few days, then you can't object to this behavior. If you don't obligate them to do more than invisible upkeep, then you also can't complain when they don't post anything, ever.

Some staffmembers--like those operating in a more technical capacity--aren't really staff in a "member relations" kinda way, so their interactions with the general population may be more at-will than the rest. Ultimately, if you don't make rules, there's nothing to break, and your disappointment will be your own. If you just expected your hires to "know" what to do, while you sit back and count your revenues, then descending from Olympus when you've got an issue is probably going to be too little, too late.

The solutions for these? If you have the time, make manuals or shorthand rulebooks for each staff type you have. Only elevate from within, where the community's idiosyncrasies and trends are known to that person already. Most of all, gain a positive, pro-social act of commitment. In writing, if possible (and keep on file). Let THEM make their goals, set the expectations with mutual respect, and when trouble arises, ask them how they would react to someone who hasn't done his or her job. If their response is "I'm busy," then you ask for more warning of that in the future, if it's acceptable. It's when they keep getting busy that you know your board, and their jobs, aren't a priority for them, and it might be time to give them the freedom to be regular members again. You never know. They might thank you.