Are you saved inside or outside of the daycare building? If you're saved inside, the NPCs will behave differently when you walk outside depending on how many PID frames you advance. It's possible that they would behave in such a way as to make certain frames unhittable.
I don't think you want the details (see the research thread if you do), but using an everstone changes the way the egg frame is constructed (one extra RNG call before IV inheritance and PID generation) so it indirectly has an effect on what PID you get. The PID itself is not modified based on whether the everstone takes effect or anything like that, however.
I'm saved inside due to having to advance the RNG Frames. I can see that the person is moving in a certain way every time, so that's the only explanation I can go off of. Thanks!