My mother is 82, diagnosed with Alzheimer’s and COPD. She has recently started staying awake for 23-47 hours straight. No sleep whatsoever.

Agree with Alva - the doc should be able to prescribe some meds so she can sleep. You don't indicate whether you live with her or not, but if you do, she needs to sleep so YOU can get adequate rest. This is not sustainable.

Sleep pattern disturbances are VERY common indeed, in ALL stages.
I would discuss options with the doctor, especially with the complication of a COPD dx. I wish you good luck.