Petra5ed,
Are you and your therapist doing good work together at all?
I hope you talk to him about this. When you say he doesn't know how it feels-have you ever told him how it feels? That is seems like he doesn't care? That you hate feeling so needy? When he mentions he wants you to be more vulnerable-do you have an example? Would you tell him you are mad at him for leaving you to feel abandoned? That when you let yourself be vulnerable by reaching out to him, that it hurts when he doesn't respond to your e-mails for days?
Sorry if that was a bunch of annoying questions, that by the way, are mostly to think about rather than answer... These are routine discussion issues in my therapy. It really, really helps to talk about this stuff directly. But there's a lot of transference interwoven throughout these topics.
The e-mail issues don't sound like transference. Many people consider e-mailing taxing, and it's not uncommon to ignore them or check them infrequently. Can you talk to him about texting instead? Most people have their phones on them at all times, so texts invite a timely response. And they are short/less taxing...
It sux to feel abandoned and uncared for.

No, umm-5 times a year is not over-dependency. And if it was-so what. If you started doing it every day, which I highly doubt, it could be addressed at that time.
My therapist would never leave me in crisis like that. He is always there for me. My former therapist would not answer my texts all of the time; however, I trusted that he would be there for me if I REALLY needed him. He said I was perfectly capable...although he was accepting of the dependency all around. I feel like my current therapist encourages dependency, but he never abandons me (that doesn't mean I never feel abandoned, because I still do at times). But yeah, I have allowed myself to become sooo vulnerable and needy with him. It can be scary.
I don't agree with others here who say that texting or calling a few times is unethical or unprofessional or xy or z. My therapist is both ethical and professional, but sometimes checks or his phone in sessions, and had to text once. Former T did the same. It actually felt good that he was comfortable enough to talk to his wife on the phone in front of me (although it only happened a few times over the years). All idealizing aside, I know I do defend my therapists. But you have to look at the whole package. So back to the original question-are you two doing some good work together?
I'm sorry you are so down and out. It hurts to feel abandoned, insignificant, unimportant...neglected...uncared for.