My word to you is persevere. Keep appealing. Those long term care insurances were bad deals from the very start, in my humble opinion. They frightened people with scenarios of ruining their finances with long stays in nursing homes, back when nursing homes were a thing to be feared anyway. Well intentioned financial advisors told people they needed this sort of policy. Those of us who worked in social services thought otherwise, for the most part. In what I have seen thorough the years, most of the people who had this type of insurance never used it, after paying them loads of money for a long time. And when you do try to get the benefits, they bend every possible condition and rule to try to make it almost impossible to get them to pay up.
I believe that your only recourse is to persistently appeal, challenge, re-apply, etc. Their thought apparently is that families with a terminally ill person are not going to want to go to the trouble of fighting with them. I watched my family members go through this, and actually, if one of the children had not had a long work background in rehab, social services and insurance, I doubt if they'd ever have gotten a dime, after my aunt and uncle had paid in thousands and thousands of dollars. Thoughts and prayers going out to you, I really hope you can get this seen through. They need to pay off.