Mom cuts her nose off to spite her face. Where she is now (like the last one) has activities which she piously and haughtily refuses to participate in. They offer to take her outside on nice days, out for a BBQ (which I reacquainted myself does not always mean spare ribs, pulled pork, etc.). The only one whose fun is being ruined is herself. Just sit in your room, contemplate your navel and your tv. No skin off my teeth. At least I'm on notice if she complains about 'nothing to do.'
If you can do something constructive, such as arrange a psychiatric workup as Babalou suggests, or have a conversation with the activities director requesting encouragement for mom, then do it.
If there is nothing you can do, or you've tried everything that seems reasonable, let it go. Mom is allowed to navel gaze. Sad, but true.
My brother - who I won't go on about but he wasn't involved, shall we say - did have one sporadic anxiety about mother - he feared that she must be bored. He bought her good earphones, so that she could listen to audiotapes or her tv or radio easily. He even threw in a couple of CDs that twenty years before she might have enjoyed. He couldn't believe that she could sit in her chair and sleep or do nothing, day in day out. I think he half suspected that either I was drugging her or I was so horrible to her that she was too afraid to ask me to take her out.
The sad reality was that she was worn out, fed up and - yes - depressed. Treatment for depression worked in that it helped her get over the worst stage of silent weeping which had alarmed even her. But everything else I could suggest - Singing For The Brain, trips to shopping malls, church festival services - she said were nice ideas, and "we'll see." I.e., no. She didn't want to. There wasn't anything to be done about it.
So, yes, it is official. Your mother is welcome to join in a wide range of well-run and pleasant activities, hosted by nice people. But she doesn't want to. I agree that it is tear-jerkingly frustrating, I agree it would be a good idea to get her mental state assessed (how can it hurt?); but also perhaps console yourself that what she does want is peace and quiet and her own company. And you've provided her with those too, in a safe place where she still has options should she change her mind. You've done good. I'm sorry it hasn't made more of a difference.
If your mom's desires have passed beyond this ability, that is officially too sad.