A recent update to TicketSource enables you, as the event organiser, to assign a start and/or end date to customers with membership numbers.
This will prevent members from making bookings outside of their membership period. The start and/or end date can be specified by modifying a customer's record via the Customers | Find Customer menu option on your dashboard.
As shown in the image below, when viewing the customer record, tick the 'Membership starts' and 'Membership ends' boxes and then enter the dates to determine the customer's membership period.
Consider sending out a MailChimp campaign to alert your customers when their membership is due to expire. You could even offer a discount on early membership renewals or rolling membership signups to encourage your loyal customers to continue their membership.