No, JFK's statement has not lost its relevance. It is still just as important today to do something for your country instead of expecting free handouts from it. But many people don't see it that way, that's the problem. We have created "welfare mentality" where people just want to receive free money and do nothing.
President Kennedy's statement still has a lot of value and relevance to today's society. There are a lot of people who still strive to serve their community and make America a better place to live. President Obama is part of that legacy, and its something the current president openly recognizes.