We had a guest at Adagio suddenly realize that his passport was about to expire - he managed to get through check in by downloading his boarding pass in advance the night before and only taking carry on so he wouldn't have to talk to a gate check in person - your biggest risk is that the airline refuses to take you on board because they are liable if you get turned down at your destination - having said that BVI is pretty lax but there are many countries in Europe which insist on 6 months before expiry.