Everybody's relationship with their therapist is different, so it's tough to say what would or wouldn't be appropriate.

My current therapist and I have no contact between our sessions, and it can sometimes be tough to wait when our breaks are longer than normal. I'll wind up having a big pile of notes of what I want to discuss by the time the next session comes around.

But I think it's important to let them have that time for themselves. Being a therapist must be a very emotionally draining job. Like us they are only human, and also like us they have their own share of problems to deal with in life. Their job requires them to set aside the problems they are facing in order to help us tackle our own issues, so they need to be given some "me" time where they can focus on themselves. For that reason I lean towards the opinion that contact between sessions shouldn't be made unless it's an emergency.

Again though, everybody has their own relationship with their therapist. I'm only coming at it from my own point of view and from my own experiences with therapists.