We were scheduled to travel from Miami, FL to Santiago, Chile On November 9,2022. I got sick on the way to the airport due to cancer treatments which caused us to arrive 1 and 12 hours before our flight. When we were checking in at the LATAM counter we were told that the flight was closed and we could not board. When asked why, we were told that because we weren’t there three hours before our flight departure time. They were not able to find us another flight that would allow us to make our trip to the Falkland Islands that we planned for over two years. We never heard of anything so outrageous. We tried to speak to several of the LATAM staff but they were all very rude and unhelpful. We will never fly LATAM airlines again. Reimburse our flight cost and the cost of our trip. Also implement training for their Miami crew so something like this could never happen again.