No. Once you purchase FanDraft, you can use it as many times as you would like, for as many years as you would like.
FanDraft has come out with annual upgrade every year, which includes new features and an updated NFL Player Database. Registered users can purchase the update for a discounted price.
FanDraft WEB is only compatible with the current season, so if your league utilizes the WEB add-on, you will have to be using the most recent version of FanDraft and FanDraft WEB.