What do we do with our mother who insists that nothing's wrong with her, but is showing definite signs of dementia?

Try to stand back for awhile, and then when you approach her again, do so with more tact. People are often defensive about any hint there is a mental issue. It's terribly sad, but there's still a stigma attached.
Is she on medication for other illnesses such as high blood pressure? Diabetes? Anything at all? Take whatever you can and suggest that she get a checkup for the problem. Then you can call or write the doctor ahead of time and tell him or her about the cognitive issues.
Also, her medications or an infection such as a urinary tract infection (UTI) could cause the symptoms you describe. So the idea is that she needs a physical. If you can get her to a doctor for anything at all, you can let the doctor figure out what's wrong. Good luck,
Carol

Thank you so much for your prompt reply. She doesn't take any meds since she won't go to a dr. unless she thinks she's dying. She has complained to my brother several times lately that she hasn't felt good so I'm hoping he can get her to the doctor soon! I live 3 hours away so it's hard for me to get there.