You do not have to belong to the club to be eligible for the $59 fare. I thought the same but called Southeast and was told by their representative that the $59 fares go first and as the plane fills up, the seat prices go up.
I purchased our tickets for early March in October/November. So, the earlier you book, the better fare you will get. We got the $59 each way fare. Quite a savings when 4 people are flying.