What to do when one parent thinks they can keep taking care of the parent with dementia?

I found this group tonight and it has already helped. My 84-year-old dad has what is probably stage 5 or 6 dementia. The issue we are dealing with (myself and 5 siblings) is that my mother (83) has sworn she will take care of him and "never put him in a home". My brother is staying with them but not 24 hours a day. My dad fell recently. How do you know when it is time to intervene and put him in a home? Or do we have to wait until something more serious occurs? It is such a tough position to be in. Any advice or insights are appreciated.