The gift certificates screen is a list of gift certificates that have been sold. It is not intended as a method of tracking them.
When they redeem the gift certificate, the intention is to take it away from them, and refund the change in cash, or by issuing a new gift certificate for the remaining amount. Some stores might redeem a partial gift certificate, and then write on the back of it the remaining amount and sign it.
A gift certificate is an item that has a value of (for example) $20. If they lose it, it is the same as losing a $20 item. You may choose to reprint the gift certificate for your customers, but there is no provision in the system for doing so.
Gift Certificates are not Gift Cards that work like a debit card and carry a balance. This feature is planned for a future release of QuickStore.