I see my psychiatrist every three months so obviously not that often. She works Monday to Friday mornings in a hospital and then she has private consultations on Monday and Wednesday evenings. She goes on holidays here and there, nothing outrageous.
But my ex T used to take a lot of vacation. I'm talking like A LOT. Like more than 3 months in total every year.
It was just too much imo. Your situation with your psychiatrist would really bother me: consistency is important and you clearly often need refills. If it's possible to find a new one, I would.