If you know a relationship is probably not going to last but you still enjoy every second of it, should you continue having that relationship?

I guess it depends on the person. It depends on if both parties feel that way and what the benefits are. If you are looking for that "forever relationship" but you are hung up in the moment, that relationship that you are really seeking may walk right past you because you are otherwise occupied. The only person who knows what is important to you, is you. Decide what you want and go for it. Your actions determine your future.