To keep a friendship going with a mom, you have to think like a mom: be flexible, multitask if possible, and find humor in sh*tty situations.
1. Invite mom for a walk/run. C'mon, you both need to get outside for a bit.
2. Go to the park with the kids. Nicely explain you just want to catch up with her so you'd prefer to sit away from the other moms.
3. Have dinner delivered at mom's house. Ideally, the kids will have just gone to bed. You arrive with a bottle of wine and some menus of restaurants that deliver. This way, there's no cooking, no babysitters, and the parents can fall asleep immediately afterward.
4. Send an occasional thinking about you email/text. Did you just hear that song that you both loved lip syncing to? Take 60 seconds to let her know.
5. Plan a girls only weekend. With no kids or husband around, it's that much easier for mom to channel her life Before Kids. Be prepared though, that you'll have to do almost all the planning. And if more than one mom is coming, coordinating all their schedules will be only be slightly less complicated that coordinating a space shuttle launch.