As mentioned, most places are using a provider sign-in/sign-out process. When you leave, you remove them as designated provider. If you have a specific designated provider growing for you, be sure to - between trips to co-ops that use such a process - fill out a designated provider form again so that your original provider can legally continue growing for you.

If you go to a co-op for medicine and they insist on keeping your original authorization... my advise is to go elsewhere. It is not necessary for them to have your original, and if they refuse to give it back I, personally, would call that theft. There are good co-ops providing good medicine that do not take your original from you - call around to various places before you go in and find out what their policies are.