Is there an extension to apply users when purchasing an item into a special membership for a certain amount of time?
Not that I am aware of, however this is one called Rewards Points that might work for you. Just look in the extension store
Here's the link:
http://marketplace.abantecart.com/?mp_token=dobv7rekar980i1jotdr0fn0q2&mp_hash=349aa054a46bf1dbd59f8e6981fc3039&rt=product/product&product_id=154 (http://marketplace.abantecart.com/?mp_token=dobv7rekar980i1jotdr0fn0q2&mp_hash=349aa054a46bf1dbd59f8e6981fc3039&rt=product/product&product_id=154)
one more extension Customer Group Update (Customer Loyalty) (http://marketplace.abantecart.com/customer-loyalty-discounts) allows to set up auto-update of Customer Group based on total amount spent by customers.