I had a similar problem with my therapist. I've been seeing him for almost four years now and always the last appointment of the day. It got to a point where he would get testy with me and lose patience and he would yawn a lot and when he realized that it was causing problems he asked me if we can move to first thing in the day so that he would be more alert and have the patience for me that I deserved. We made the move to first thing in the morning and things have been great ever since. I can understand how some therapists will lose patience at the end of the day especially if they have some very difficult clients before you and I know my therapist had one right before me she would always be late come out crying one day there was an emergency so I know it was not easy on him with her. You may want to ask if you can switch to an earlier time might make all the difference in the world.