I wouldn't message her for her birthday either.

I understand the need for space when depressed - I need it too. I just can't imagine telling someone I care about that I wanted zero contact with them. In fact, I personally crave contact with the people I care about when I'm depressed, even if I'm terrified of destroying things with them!

If she wants zero contact with you, then it's over. If for no other reason than the fact that you don't deserve that. No matter how depressed she is, she can't just erase you from her life and then pick it back up later when it's convenient for her. Relationships, and friendships, require taking care of each others' needs - she's completely neglecting yours.