When I was using the Figure platform in my previous role, and a customer requested their wine club membership to be placed on hold, I would remove them from the club membership completely, via the "Cancel Membership" button. Then I would put a note in my calendar to contact the customer a couple months after an upcoming club release to see if they wanted to reactivate the membership. 

All their information will still be available in their account so it is easy to load them back in to a club at a later date. Plus, contacting them before an upcoming club release will give you a chance to check if the shipping address and credit card in their account are up to date.

It is best to remove them from the club even if they request to just put it on hold.

I always wanted the number of people in my clubs to represent the actual buyers, which helps to assess production quantities and upcoming order totals on deck. Most wineries and wine retailers have club goals and if you leave non-buyers in the club it will skew your projections. Further, it would turn into a cumbersome task keeping hold requests in the club and having to remember who not to charge during the batch process. That can be risky.