Can you let them see the progress you have made? Then they'll understand that you will come out of it.

Also, reframe it. You're doing what you need to do, saying no, and that's what your friend is doing to, trying to avoid your rejection. It could be that she's starting to take it personally, and avoiding the rejection by checking in less often is her way of not being hurt so she can continue your friendship. It sucks, but it might help you to see it as her taking care of herself. And when you're feeling better, you can contact her. She's not saying she doesn't want you in her life, she's saying right now it's hard for her to keep getting turned down is all.