My father is in stage 5 Parkinson’s. He has started falling a lot & cannot remember to push his button for help when he wants to get up.

The only way to have someone with him 100% of the time is hiring someone. Even nursing homes do not have one on one care. It can be very expensive but worth it. Sorry you are going through this is so hard to make decisions like this one.

The reality is that people still fall in nursing homes, and unless they fall where they are among other people they can still lay undiscovered until someone checks on them. If he is doing fine at home you could look for one of the call buttons that have fall detection built in and call automatically when a fall is detected.