When playing in a long-term save you will notice the calls to ask to stay over never happen. However in a fresh save you will receive calls, until a point happens where no stay-over calls happen ...
Ideas
It's such a bummer this doesn't work the way I think it should. It would be nice to have grandparents call and ask to come stay over and help take care of the little ones but it just stops working after a certain amount of time.
In my current save I had it happen right away. Loaded the game up and when Growing Together came out my Sims parents called to say they wanted to come over and help out with the little ones. My household didn't have little ones but I was excited to see the call none the less.
After that I never received a call from anyone asking to stay over. Even though it's a setting in options no one calls for those kinds of invites in existing saves at least.