I don't keep my fish QT running 24/7 like some do, it's actually is better to break it down and clean it well between uses.
Coral/Invert QT is a little different, as it should be kept as stable as possible. Basically just a second, fishless system. You can keep inverts/CUC in there and feed them periodically if you aren't using it for coral at that given moment. And make sure to keep up with water changes and such... just as you would a display tank. Ideally, you would want your parameters in coral QT to be as close to those in your display as possible.