It's an interesting question, and the answer probably lies in your state statutes. I am not licensed in Alaska. However, by way of comparison, here in PA, if I am required to file an answer or other court-related document by a specific date (let's say, the 15th) my document is due by close of business on the 15th. As more jurisdictions turn to electronic filing, that opens the available filing date/time up until 11:59 on the date the document is due.
So turning back to your question, unless there is some specific provision in a statute relating to bailment, stating that the 15th ends at midnight on the 14th, I would say that your pawn shop is probably incorrect. Depending on the value of the items disposed of, you might want to contact a local attorney to discuss this issue and to try to determine if there is any cost-effective recourse for you.
This answer is general in nature and is not intended to nor does it create and attorney-client relationship. If you have any further questions on this issue, you are encouraged to seek the advice of an attorney in your state.