I've had friendships that have drifted apart - and I've been on both ends - the one left behind, and the one who moved on. Sometimes jobs or lifestyles or life in general shapes us and we end up slowly adapting to new things or growing out of old things and looking for new things. Don't take it as an insult if she's not wanting to hang out so much - it might just be that she's looking for different things in her life now. There are so many influences that you may not see which are driving her down the path she is on. But it does sound like it is time to let it go. I agree with Fourteen and I personally wouldn't bother sending even a happy bday wish. What you need to do is find something else to keep you busy and even if the one time she calls and you aren't busy, fake it anyway - you need to cut the emotional ties and she needs to see that you aren't always there waiting on the shelf for her when she decides it's convenient for her to be friends all of a sudden.
I think you need to hold your chin up and start letting go. It won't happen overnight but if you want to salvage even the tiniest bit of your relationship with her, make sure you aren't coming across as being clingy and just let her have all the time she needs even if it is months and months. And put your family first - don't let her be disrespectful in your house. It is time for you to set your boundaries, too. She sounds like she is going thru some stuff - don't get sucked in. You can be supportive, but don't go chasing her around. Part of life lessons is learning how to 'be' a friend and not just 'having' friends - and this is a lesson she needs to learn. But for what it is worth, hang in there. It doesn't feel all that great right now but it will get better. Relationships (especially BFF breakups when they happen) are hard work.