Why would a nursing home rehab facility kick my stepmom out after 9 days when Medicare says she has 20 days paid for rehab?

Being in rehab is not approved automatically for any number of days.
The number you mention is the maximum for a patient requiring rehab care. These are reasons for discharge from rehab:

1. Patient is unwilling to cooperate in care and is unable therefore to make any progress.
2. Patient is unable to cooperate in care due to dementia or other concerns, and therefore cannot make any progress.
3. Patient has made all the progress that can reasonably be expected in present circumstances and is ready for either placement or homegoing.

The assessment is done by the trained personnel at the facility. Once they deem a patient ready for discharge the bill will no longer be paid by Medicare or Medicaid, and the patient will be "self-pay".

Just know that just because you QUALIFY for 20 days doesn't mean they want you to USE 20 days if either you CANNOT improve, or cannot work with them, or have improved all you can improve.
Medicare is saying "If you NEED this time, you have it", but it is not saying "We WANT you to use this time".

Rehab is paid for only as long as a patient is making measurable progress. If a patient has progressed as far as possible or refuses to make an effort with rehab protocols, he or she will be discharged.
Rehab is not an automatic holding area even for the number of Medicare "allowed"days.

If insurance or Medicare find that she's improved all she is going to, or if she has stopped improving, or if she declines therapy, they will quit paying.

Medicare will only pay the rehab bill as long as the patient is making progress. They are in constant contact with the rehab facility to make sure this progress is being made. As you said, your mom stopped making progress, so Medicare stopped footing the bill. You can assume the bill yourself now, which seems silly if she's not making progress....and that's how the insurance nonsense works, unfortunately. My father was booted out of rehab in short order too. With mom, I told the physical therapist she'd be wheelchair bound for GOOD so please work with her on learning to "walk" within the confines of the chair, and help her build her arm muscles to propel herself around. So that's how she stayed in rehab for 20 days w Medicare footing the bill.

100% if she is considered non-compliant with physical and occupational therapy - it does not matter what Medicare has approved - they can and will discharge her. The approval from Medicare is just authorization from them for what they will cover as long as she is continuing to make progress within the PT AND OT's prescribed rehabilitation program for her. If PT and OT do not feel like she is working with them and they have seen several successive days of her refusing to participate in their care plan for her - they will discharge her as "Nursing Home" level care - at which point - Medicare will no longer cover her time in the facility - which is when either their daily rate kicks in or she has to leave.

We encountered this several years ago with my FIL. HE maintained that he was doing everything that he was asked to do. I guess technically that was true. Because after day three of him literally beginning the "I'm in so much pain, my arms hurt, my legs hurt, my back hurts, my (insert body part here) hurts" the moment PT or OT even opened the door, they stopped ASKING him to do anything more than basically wiggle his toes or fingers. HE thought he had it made - he didn't have to do much of anything and he seemed to think that he was appeasing them. What he didn't seem to realize was that he earning himself a fast pass right out of the door and ruining his chances at a true rehab.

PT and OT cannot run the risk of injuring their patients, so they can only do what their patients are willing to do. If their patient displays reluctance to do as requested, they can nudge and try to work with them and encourage them certainly. But there is a line. And after a certain point, they have to stop - no matter how much they want to help or believe that there is a possibility that the patient can be rehabilitated, because they have a liability issue. They cannot FORCE them to comply. They will do what they can within certain parameters, but the real rehab, for those patients, ends up stalling out and they don't progress the way they could have, and end up being discharged way before they could have been if they had really committed.

That rehab stay ended up being the start of the downhill slope for my FIL. It was the very first of several "non-rehabilitatable" stays in rehab before he was finally transferred to a nursing home a couple of months ago - because he just never wanted to really do the work to get himself better. He had the capacity, he just never wanted to try.

As far as who makes that decision - it's the rehab and Medicare. Medicare goes by what the PT and OT say as far as their progress. Medicare is not going to pay if someone is not progressing. And they only have a certain amount of time to show progress or an attempt at compliance. My FIL the last time was in and out in 10 days.

This very same thing happened to me with my father. He had time left on the rehab days from Medicare, but they were downgrading him to board and care. They too said it was because he wasn't making progress and unless I was willing to pay cash for him to be there in the rehab, he was going to be downgraded.

My father's Medicare and secondary insurance already paid for the full number of rehab days.
The facility was trying to work the old "double-dipping" nursing home scam these places are famous for.
They got their money from insurance but still tried to collect it in cash from us.
I don't think so.
I had a nice talk with the good folks at Medicare. They didn't know anything about it and were very interested to hear what I had to say.

The rehab doesn't want to reveal any information to you because they are probably working the same scam that they tried to work on me when my father was sick.
Whatever you do, please don't pay them anything in cash until you talk to Medicare and get it in writing exactly how much they have paid out for his rehab care. If it turns out he's paid up like mine was, then he stays in rehab longer.
Good luck.

Medicare is willing to pay for 20 days assuming that progress is being made with your Mom. The PT in the rehab hospital is the one who writes the reports and indicates progress or not.

Even though your stepmom is out of the rehab hospital now, I would ask to see her records to determine what occurred to have them state that she is not making progress. Could they have just wanted to stop PT because their expectations were too low for the age of your stepmom? (For example, they didn't expect your stepmom to be able to walk, and she was walking.) Could she have been a high maintenance patient and they didn't want to or could not spend the time that she was demanding? Could she have been refusing to see the PT or do the work that the PT wanted her to do?

...and I hope you got her out of there. Four years ago, when my 97 year old Mom was in the rehab facility, the PT determined that she shouldn't be walking at her age and therefore, she was completely cured. Therefore, Medicare stopped paying. Because I was away and she couldn't be discharged to a person, we paid the full fee. During the remaining 1.5 weeks she was in the rehab hospital, the PT never visited her again. Exercising completely stopped. Therefore, when I came to get her, she was completely confined to a wheelchair and couldn't stand up on her own. I found a PT who was willing to try to get her to walk again and she did within a month, completely not using the wheelchair within 4 months....at the age of 97. I'm still ticked at that PT in the rehab hospital.

So It is worth your while to find out what happened for the decision to be made that she could not be helped anymore. You might need that knowledge for the next time she goes into the hospital.

P.S. We now have a PT person who makes home visits. Medicare and my Mom's health insurance pay for it , when we need it. My Mom will be 102 within 2 weeks, and she is still able to walk short distances with a walker.

JoAnn29 where my 60 days comes from is my wife had a major operation and after 5 days in Jefferson hospital was released to the Acts/Evergreens for rehab she was there for 60 days. Medicare and my supplement paid for everything. We did not receive a bill for anything. I cannot say enough good about the Evergreens. This was back in 2021. I just googled how many rehab days does STRAIGHT MEDICARE pay for in case there was a change since we used it. The answer is 60. I do not know anything about advantage plans.

Could be they had a better paying client who needed. 60 days - these places are for profit and it’s about keeping the beds filled . My mom stayed in one for almost 100 days and she was not doing her physical therapy - they released her and said “ she was independent “ no she couldn’t walk and was incontinent and had terrible dementia