My mom has some established "red" Autumn Joy that seems to be withering away while her other "blue" & "white" established Autumn Joy is doing fine in the same area. Here are some photos that show what is happening. The first photo below is how they begin their demise & the second is the death spiral. Does anyone have any ideas about what could be causing this?

Are you where there's been a ton of rain lately? If so, could be too much for Sedum, which likes more dry conditions. To save what's left, you could cut off any still-healthy looking parts, let them dry overnight in the shade, stick in the ground in a more sunny/dry spot.

The plants are in Southern Illinois, so they have a lot of clay and humidity, but the dying off starts before it gets to the high humid days of summer. They usually get quite a bit of rain in the spring so a lot of moisture is held because of the clay. It doesn't seem to affect the white and blue autumn joys that are planted close by. Mom did take some cuttings last year and moved to a new bed that has a lot more aeration and compost to see if that would make any difference, but they are once again starting to die back.

I seriously didn't think there was any way to kill "Autumn Joy" sedum... but then, I didn't know there were blue and white versions, either

Dig it up and see if the roots are being attached by some kind of grub, or other pest.

Thanks for the suggestions! I'll have mom dig & take a look.

Oops, that reminds me I have one I need to dig up. Just this one, Sedum 'Touchdown Teak', all of the other sedums are growing well and very healthy.
If I find anything I will report back here.

You say the bed has compost? The compost may be holding too much moisture. The sedums prefer rather spare soil. Fertilizer can cause them to rot and die.
One year when we had heavy rains, mine flopped over, laid on the ground, and rotted at the base. They then rooted along the stem. I guess it was their way of dividing the clump without my assistance.