What are the factors that determine if my elderly mother should be driving?

Many people with dementia retain learned skills and are able to drive safely for some time after diagnosis, however, as dementia progresses it has serious effects on memory, perception and the ability to perform even simple tasks, and eventually they will lose the ability to drive, and the stage at which this happens will be different for each person.
Giving up driving is not always an easy decision to make, some of them may be very reluctant to stop driving, so then they may need some encouragement from their family and friends, but still this can be a very difficult and upsetting situation.
You can try to explain to her your concerns about her unsafe driving, giving specific examples, and ask her to voluntarily stop driving, and assure her that the ride will be available if she needs to go somewhere. Also you can ask the doctor to advise her not to drive.