If it's your insurance policy or therapist, don't think there's much you can do about it? I would just try to use the constantly shifting day/time to my advantage; life has a lot of change we can't control, I'd work with the appointment thing the same as I did my T going on vacation.

I had a T in private practice so could see her the same time every week. It was hard for me when we changed times, or days, or locations; the mind gets use to the "habit" so easily but I think that can make other things more difficult. I think you have to compare insurance/clinics with rules to each other, rather than all T's as those in private practice are free to do what they want whereas your T is not.