I haven't read the other responses, so I may be duplicating them.
It wouldn't hurt for your mom to be checked for the Nasty A, but it would be better if it were her idea - to get checked to be sure she *doesn't* have it.
I'm, um, a few years younger than your mom, and I do strange forgetting things. That's the reason I had six new jars of ground cinnamon in my cupboard at one time. Do you know how many loaves of cinnamon bread have to be made to use up six jars of spice? But when I went to the grocery, my brain kept saying, "You need it," instead of "You've bought it," because I wasn't working from a grocery list. I'll rush around putting things away to tidy up, not really thinking about what I'm doing, and later on I'll have no idea where I put those things. (I should have paid attention.) And, of course, calling the children or grandchildren by each other's names....
I dare say your mother is worried about Alzheimer's. Everybody from age 45 up seems to be worried about Alzheimer's. That could be where her defensiveness comes from. Let her know you love her and want her to be the healthiest and happiest she can be. Let her know that if the A. were to happen to her, you would still love her and you would never let her down.