My mother is in mid to late stage vascular dementia. Her latest thing is that she will end up on the floor (I don't think she falls as there are no injuries) and say she can't walk. My dad will call me to come pick her up and there are times when I get there she has gotten herself up and walked to another room. This goes on several times a day with her not being able to walk and suddenly being able to. Is this from the dementia (she has a history of attention seeking)?
My husband wouldn't use a walker, either. And he had these falling episodes even when he was using it at my insistence. To my great surprise he was very willing to use a wheelchair -- perhaps in part because it gave him confidence that he would not fall. Perhaps you could get the loan of a wheelchair from Goodwill and try it out for a while as an option.
What does her doctor say about the falling?
My suggestion would be for her to use a wheelchair. If she has the strength to "walk" it with her feet or roll it with her hands, she can get around fine in the house with greatly reduced risks. If she doesn't have that much strength, could Dad push her?
Since these spells of immobility seem to wear off, another suggestion is to persuade her to stay on the floor until she feels stronger. Offer her a pillow and possibly a blanket.
My husband had episodes of falling, not being able to get up, and then after a period being "fine" again. In his case it turned out to be narcoleptic-type episodes, where his body was literally falling asleep mid-step. When the episode passed he was back to his baseline for strength and mobility. (It was very hard, though, to persuade him to just be calm and wait for the episode to stop.) Until we got a diagnosis a wheelchair was a huge help. Once it was diagnosed a medication was very effective.
If it is possible to observe some of your mother's episodes as they happen, a detailed description can help her doctor come up with a treatment plan.