Can you tell your T what you posted here? I think the problem is that, by support, you mean that you want an immediate email or phone call from her.
Most Ts won't do that. If it's urgent, they would want you to schedule another session. I think that each time you say you've resolved the issue with your T, you really haven't. You will still email her, and will still get hurt if she doesn't respond as quickly as you want her to. Can you and she work out a definite arrangement regarding emailing, or phone calls? Maybe phone calls would be better than emailing . You said that she said emailing isn't so good for you because then you don't TELL her in person what is wrong.

I understand your needs and your frustration, Peaches. I wish there were a really good solution, but I can't think of one.

Maybe you have to sit with the feelings of being abandoned and hurt until you get to your session, and then work through those feelings with your T instead of in an email? I know you're working on the DBT skills, but this sounds like something you need to resove with your T. I'm sorry you're still struggling with this.