I now have a regular time slot but I have had a moving slot with a previous therapist. Either can work for me but I have learned to have them write the moving slot down after we had miscommunicated about dates and times, so then when it happened again - I had her card with her handwriting to show that I was not the one who had screwed up.
I will say, that even the therapist now who is iffy in terms of competence as a therapist, she has, at least to this point, kept the slot I have pretty much for me. Sometimes she cancels, but I do not think it is because of giving the slot to someone else. Although it may be. I never really thought that if she told me she had to cancel that it was because someone else was in the slot.