I’m having the same issues. In fact, it’s killing my game every time my airport gets to a certain size. I have staff rooms all over in both secure and non-secure zones. At one point I built specific staff rooms for ramp agents and airport staff right next to the gates. No dice - the staff would never show up on time, my flights got delayed, and the Flight Planner got inextricably screwed and, no matter how often I saved and restarted, flights would show up on the planner as enroute as much as a full day behind the Planner schedule. I tried cancelling the flights back in the past so that the upcoming flights would be the only ones occupying gate slots, but all that did was stop all traffic coming into the airport at all.
It’s a real shame, because this game is really, really amazing… up to a point. Past that point, it becomes a nightmarish waste of time. Hoping further development happens to solve this.