How can I convince my 77-year-old mother to go to the doctor for her memory problems?

In the last six to 9 months she has had short term memory problems, repeatedly asking the same questions, misplacing items, forgetting recent conversations, the day and the month and ages of grandchildren etc. She is a very proud and self sufficient woman and does not have mental issues such as depression or mood swing problems. Her mother had coratid artery blockage at this same age. She does go to the doctors every six months and is a good patient, but refuses to make an appt. sooner for memory problems and is obviously scared of the outcome. My brothers worry about upsetting her because when we initially suggested she see a doctor six months ago, she was very hurt and angry with us. Now when I delicately try to encourage to make an appointment for this issue, she blows me off. Your suggestions would be greatly appreciated as she is the heart and soul of our family. Thank you.