I am sorry for your loss. Losing your mother is one of the most difficult events in a person's life. I am truly sorry.
As for the insurance policy, it is basically a contract between the company and your mother. To give a more accurate answer, an attorney would need to look at the policy and see if there is a provision that allows for a late payment or some form or manner to bring the policy current in case of incapacity. I have doubts that such a clause would be in there, but it never hurts to look. Unfortunately, her belief that she made the payment is of no consequence.
You have to check Missouri law on life insurance and insurance regulations. Send your question to the state insurance department or insurance commissioner's office. Most states require written notice of cancellation, grace periods, and provisions for failure to pay due to incapacity. You can check it out yourself but if you do or don't find a loophole in the insurance company's denial, it's still recommended that you consult an insurance lawyer to make sure that you've done everything possible. This advice gets more and more critical as the face value of the insurance goes up. If the insurance is for $50K or more, you would be foolish not to investigate thoroughly and consult a lawyer.
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You should contact an attorney immediately to discuss this case and provide the specifics.
See the below information regarding whole life insurance policies:
In most cases, you have a 30 or 31 day grace period to make up for a missed payment, so even if you are late, you can keep the policy in force by catching up. According to the American Council of Life Insurers (ACLI), if a policyholder dies within the grace period, beneficiaries still receive the benefits left after the overdue payment is deducted. But if the insured person dies after the grace period, beneficiaries do not receive the death benefit.