Any advice on appealing for extended care?

Were you able to see her fo therapy and/or talk to her therapists.

Sometimes, clients don't want to get out of bed as one example to do therapy, especially if they are in pain.

I agree with JoAnn29 that the patient needs to be progressing, or at least cooperative. PT is medically assessed and needed by her doctor ("prescribed" so to speak). There is an appeal process, the one I dealt with in a rehab center in FL basically didn't pan out because my 100-yr old Aunt also had advanced dementia and would barely stay in her bed, even with a broken hip. The staff can only do so much. A rehab facility is not the same as a NH, it has a specific clientele and carries out a specific purpose. It's not for general care.

Kepro is the organization that was inbetween us and the rehab center (and I guess Medicare).

https://www.keproqio.com/bene/appeal.aspx

If you feel this is still an unsafe discharge and that you cannot provide what she needs, then this signals to the discharge planners that she may need long term care. The social worker will let you know and educate you about insurance rules of what additional costs to provide care until or if she will fully recover...or not. You will find the info in your insurance plan or Medicare plan that the extra costs will be around $180 per day for a certain number of days before it becomes custodial care (nursing home) at around $350 per day. Each year those costs go up.
Early discharge can happen if she is refusing care, quitting too early, or failing to progress. The reason may be because she has plateaued and is not expected to return to 100%.

That 2 weeks is not guaranteed. Ur mother has to be cooperative. She has to be able to remember what exercises she did before and be able to listen to instruction. A Dementia patient can't do that. I was told my Mom would never walk again without the aid of a walker (already using one) and someone assisting her. She got back to the AL and within 24 hrs was walking all over with her walker.

You can always ask for in home therapy. If Medicare does not feel she is progressing, they will refuse to pay.