Yes, I feel similarly. Well...I feel the difficulty between sessions, but I haven't considered quitting because of them.
I find that as soon as I'm out her door and on my way home I start to think 'oh no, I have to wait another week before I see her again.' And I generally count the days every until my next session. I used to be a bit worried about it because it felt like I was being too attached/dependent/needy. It felt almost obsessive to think about therapy/my therapist so much. A year on, I've just sort of accepted it - but that doesn't mean it feels great, because I don't like the intensity of it. It feels almost like I'm pining for her - a real sense of deep yearning to see her. And that makes me feel a bit mortified. But I also think it makes sense - she really holds space for me with total compassion, patience and full attention and she's non-judgmental. What's not to like, I suppose?! :-)
Like some others have said, for me it's also a lot to do with things getting stirred up in session and then being left with it all to deal with on my own. I find it difficult to connect to my feelings during sessions so what tends to happen is that I'm very calm, composed and mostly pretty buoyant in sessions. Then, after session, there's always a bit of a shitstorm as I start to process difficult feelings - they're feelings I don't feel during session, they just hit me like a tsunami afterwards. It's something we're working on - she'd rather I connect emotionally and experience the feelings when I'm with her so that I can explore and process stuff when I'm in a safe space with her as opposed to leaving her feeling fine then getting overwhelmed with difficult stuff and getting I'm a bit of a state! I wonder if a similar thing happens for you?