How do I advise my mother that it is time to move to an assisted living facility?

I don't think "advise" is necessarily the best way to approach your mother. In my experience, when a child tries giving a parent advice, even with the best intentions, the parent digs her heels in and won't budge. Another way to approach this situation is for you to start making notes about the health, living habits and behavior of your mother. After you have a very clear idea of what's going on, you can slowly begin making references to moving. Feel her out. If she lives owns her own home, you can talk about the responsibilities of owning and maintaining a house. You can bring up the continued increase in her need of your time. You can then discuss your observations concerning the way she is living. This all has to be done slowly and carefully.

Let her know you are willing to take her to visit retirement communities. Make it fun. An example would be, "Let's see how many free lunches we can get!" Someone I know actually did that, and it worked!

My best advice is let her be part of this decision so she feels as though she still has some control.