How often should I answer the same question asked over and over by loved one with dementia?

It Depends On You. Answering the same question over & over & over again requires lots of patience and love. If you find yourself becoming frustrated, irritated, impatient, etc, it's time to do something else. We suggest redirection & distraction. With that said, there's no reason to put yourself in that situation. As soon as you realize the same question is being asked, start redirecting & distracting your loved one.
Offer your love. As many times as you care and love her. Even though the person may not remember or not even understand your answer, she may be able to feel the patience, tenderness, love and care you express. At that moment it can be for her like the only drop of water that falls in a very hot desert.
Within The Limits. One should answer the same question of a demented patient as often as possible given that there is no harm. If you find yourself or see your loved one becoming angry, frustrated, anxious or sad you have reached the limit. You need to change your approach. Change the subject, change the venue, distract the patient. The limit is highly variable so no numeric value can be assigned to how often.
Inability to form . memories is the hallmark of Alzheimers. So for the person with dementia it is the first time they have asked the question even if it is the 100th time you have heard it. If you find you are losing patience, try distraction, getting busy doing an activity or start asking questions yourself. Consider getting respite assistance.