@Shagga I have observed the problem you describe with Air Staging Beacons (Seraphim) and I've seen it with Aeon as well (and it probably happens with the other factions too). Until tonight I just thought they were broken and in a way (UI/UX) they are. In order to "deploy", you have to "sub-select" the individual air units at the menu presented for the repair/refuel building and then deploy. If there is a fast way to select all of the parked units at the building's menu, I haven't found it yet, I've only been able to select individually (ugh). Curiously, even "select all air units (CTRL+A)" does not select air units parked on the r/r building (which seems really broken). I would think the way it would work is that parked units deploy when the deploy order is given to the r/r building. And maybe it's preference, but when I tell air units to go home and repair/refuel, they should do their business and then get off the r/r building so another air unit can use it. It appears that telling air units to return home to repair/refuel is what causes them to park on the air staging building (and get "stuck").
I'm just getting into FAF but the behavior might make sense for something like a "hangar" and maybe there is a mod for that -- if not might be a great addition. "AHA! Feel the power of the air force you didn't think I had. Muahahaha!"