I told my T that I was committed to not quitting therapy like I have so many times in the past. She has told me, during difficult times to trust the process and don't give up. I tell her first thing is session when I am there but don't feel at all like being there. It's great that she understands what I'm going through and having it out in th open is really helpful. Her encouragement and support for my committment to not quit have been very helfpul. Now that I let her know, all I would have to do is tell her I feel like quitting and we can talk about it instead.
So yes tell her right away, "One of my issues is that as much as I want therapy and to commit to it, I sometimes have times when I want to avoid it by skipping sessions and I think I do that so that the therapist will give up on me." Then let discussion about this become part of your therapy. Your T will be very glad to know this about you up front via self-disclosure instead of having to figure it out over a period of time by you acting on it. I think you'll feel relieved to have it out there too.
Our T's are there to help with our difficulties rather than to judge us and abandon us in those times of confusion and fear.