I'm not understand why, if you would really like to cut contact or limit contact, that you would call her on his birthday to ask why she hadn't called your child.
It sounds like you need to lower your expectations. If she remembers and calls, great -- bonus for your child. If not, well, that's just how grandma is. But, to call her to ask where the call is, that's just playing into it. You are just as much into the game as she is.