Sounds like she has a massive blind spot on seeing things from other people's pov.
Everytime you give someone the flick despite having committed to a plan together and that friend reserving that time slot for you... you are sending a hard message that they are lower in your thinking/priorities than <insert whatever you spend your time on instead>
Most people would ruefully recognise that, yeah, no surprise that person opted not to be in the game with you anymore.
She's still baffled after all this time (out of curiosity did you say anything like 'well what do you expect!?') tells you she has actually zero perception of what it's like to be on the receiving end of this. Which means she doesn't see a problem with it.
So let her float through life, free as a bird, not paying heed to these things. Other people's time is irrelevant to her so accept it and don't put yourself in the position of being on the receiving end.
She'll get by on group things that she can dip out of without upsetting people enough to bin her off, and work her way through a series of one to one friendships that 'mysteriously' only last as long as it takes them to work her out.
Do your kids a favour, sit them down and talk about how it's important to know what kind of treatment is ok and you are willing to accept and what is not. This is an excellent lesson in boundaries and autistic kids often need that more than anyone.
Tell them her letting you down isn't an understandable one off, which would be fine, it's a pattern and as much as you all enjoy her company, placing your weekend plans in the hands of someone who is highly likely to ruin them is not what you are willing to accept and neither should they.
Friendship is a two way thing, and both need to appreciate each other. Appreciation doesn't look like carelessly disappointing someone.
Tell them the greatest predictor of what you can expect from someone is how they have typically behaved in the past and so you know she will do this to you time and again... And that's not ok
Tell them it's sad, but sometimes we have to make hard decisions especially when it means not allowing yourself to be ill treated.
Tell them you haven't fallen out, you may still see them at various occasions. But you won't be making any plans with her.
Or conversation to that effect.