I am concerned that we may be dealing with some confusion about the terms of the long-term insurance contract. Are you saying that the contract is limited to only providing three years of care? Or that you are only paying premiums for three years and then coverage ceases? I suspect it is the former.
When IRS Pub. 502 Medical and Dental
Expenses speaks of the contract being "guaranteed renewable," it is speaking of the term of coverage during which premiums are paid and a claim can be made. It means that the insurance company cannot cancel the contract because of your mother's age or health. If your mother's contract will provide her with three years of care, but that period can begin a month form now, three years from now, or ten years from now, as long as you continue to renew the contract and pay the premiums, that will be a "qualified" long-term can contract.