When I was with my old therapist R I needed the out of session contact to prove he was still there. I didn't have object consistency. He was unreliable and kept changing the boundaries with it though which only lead to intermittent reinforcement as I never knew if he would reply or not- so I did over email about changing my session. He used to allow it then got really strict about not replying to anything without warning or discussing. We had a rupture that couldn't be fixed so I left.

New person I'm working with actually replies when I message. Not strict about it. I know he will get back to me when he can and that creates less tension.