Confused, your therapist's burnout is not your fault! You did not push him away, he has "management" problems of his own. You are not his only client so his overwork involves more than just you needing him.

If he doesn't e-mail a date within the next couple days, you e-mail him and remind him and tell him "not too long inbetween or I'll feel abandoned" :-) or something similar so he knows it is an issue.