Hi Ezim and welcome to the forums,
I can relate to what you wrote about feeling rejected. But I am usually the friend who cancels. Sometimes I get in a place where I don't answer texts or emails or calls either.
Usually I am drowning in guilt too. I want to show people I care about them but I cannot make myself do it. It's a vicious circle too because when I feel guilty and crap for letting them down it makes me pull away further and further. Ie "they deserve better than me".
What can you do?
First of all I agree with you saying talk about it. Your friend may be completely aware of how rubbish she makes you feel. Or she could be oblivious. You won't know unless you talk to her.
Pick a time when you're both well and catching up (if you pick a low moment she may just back off further).
I don't manage this very well myself and have isolated a lot of people in my life (I'm 33). The friends that have stuck around are people that understand what to expect from me and are able to accept it. They also know I don't expect anything better in return.
One friend and I make a plan to meet up weekly. It only lasts if she tells me when and where I am to meet her. If it was left to me 6 months would pass.
Another sends me a text "are you alive" when she is getting worried and needs a reply. She doesn't care if it is a sentence just acknowledging I am reading her words.
My husband knows to call if it's been a day with no response.
I know you feel rejected. I feel bad on behalf of your friend because I get it but reading your hurt is hard.
Maybe think about what you need and expect from her as a minimum. If you can put a few realistic things in writing to give her you might find she is able to do one at least. For example if you text making sure you get a reply within 48 hours.
In the meantime what supports are available to you? Is there a local playgroup or women's health centre where you can join to meet some new people?
Has your post natal depression been managed by your doctor and yourself?
Perhaps it might hurt less if you have more supports around you so you don't notice her lack of support quite so badly.