Can my mother with bad dementia who can stand for a few seconds ever gain leg strength again?

My aunt (92 dementia) has therapy often. She does have good strength in her legs. But there are times when asked to perform an exercise by her therapist, that she can not do. The exercise. Not because of a physical limitation. More of a mental one. I also have times when I have her out and there is a distance to walk, that she will seem to freeze. It’s frightening for both of us.
But your mother would benefit from an evaluation from a physical therapist to see what’s going on. Of course the old saying, use it or lose it applies. The sooner you get her help, the better chance she has.
And standing, even without walking, is also helpful.

I agree that she should be checked out by her Dr. It could be something more than just strength, like dehydration or fear. Therapy could help.

Have her physician evaluate her to see if she might benefit from in home physical therapy.  He/she can prescribe it.  If she regains strength, maybe she could use a walker and that would be a blessing for both of you.

Not just by standing. But by walking she can regain strength, yes.