It sounds like you need to take the que from the mother and stop pursuing it. I had a similar situation where we asked a new neighbor over to play and they came once, and invited us to their home once. I then invited them a couple more times and got excuses or no response until the last minute.
It took me two cold shoulders and no offers of alternate times or reciprocate invites to stop calling. I never asked her why. Even though I was curious if it was no connection with me or the kids didn't get along, in any conversation I played in my head, I looked clingy or desperate in some way. No thanks. Although we did not know each other as long as you and the other mother. Sometimes the neighbor girls still ask me if they can have a play date, but I always tell them it's fine with me, but you have to ask your mom.
Also, could it be you are a little hurt that a woman you thought was your friend is now not responding to you? I would be just as hurt over that as the girls not playing. It seems extremely rude.
If your daughter asks again, then tell her she's growing up and can help plan her play time with friends. Tell her a play date is fine with you, but she needs to talk to her friend at school and if it's ok with her friends mom then you can get together. This will put the ball in the other court and you just sit back and see what happens.
In the meantime, focus your and your daughters attention on her other friends. Invite them over, or encourage her to make new friends and invite them to do something. We have a school directoy and my little social butterfly is always wanting me to find someone's number. I've reached out to plenty of moms I didn't know at all with "Hi, I'm R's mom and she and Suzie Q are in the same class. R would love to play with Suzie, would you like to meet us at a park?" Sometimes it sticks and sometimes it doesn't.
It's probably that the girls are growing apart for whatever reason and the mom either doesn't want to stay friends with you apart from the kids, or doesn't know how to be your friend when the girls are not friends. I'd be polite if you run into her, but don't initiate any more contact. If you keep reaching out it might get awkward.