I have never had Betta's specfically, but fish in general, and I have heard, that the often don't live as long becuase they are overfed. Do you know how much/often she is feeding the fish? I feed my fish a "pinch" once a day. My gourimi lived for 6 1/2 years that way.

The other thing may be if the water is too cold the fish may be feeling sluggish?

Hope your grandma's fish is doing better soon.