Advancing age brings its own set of problems, and knowing when it's time for someone to give up their independence is often one of the most difficult. It is difficult for you, and it will be difficult for your mother.
After all, if you were in her position (as you may be someday), you'd probably feel the same way your mother does. The reality, however, is that an older person may not realize how risky it has become for them to live alone, and it may be very hard for them to accept this fact until something serious actually happens (such as a fall or other health crisis).
While you need to be sensitive to your mother's feelings, it's important for you to begin talking with her about her future reluctant as she may be to do so. I suggest, however, that you explore some other alternatives that would permit her to stay in her home, such as having someone come in for a few hours a day to help her. Or your community may have a program that provides a daily hot meal to elderly people in their home. Friends who have faced this problem may have other suggestions for you.
In addition, pray for your mother, and do all you can to help her. Most of all, remind her that she is never alone if she knows Christ. The Bible promises, "Even to your old age and gray hairs I am he, I am he who will sustain you" (Isaiah 46:4).