I found this website through our airline: http://www.iatatravelcentre.com/ you can check your specific itinerary and it will tell you if you have sufficient travel documents for entry. We may go ahead and get it renewed just to be safe. The U.S. Department of State just states that the passport must be valid at time of entry. And the Consulate General of Jamaica website says it must be valid for intended period of stay. Better to be safe than sorry!