Yes! There is no subscription cost associated with becoming a member - it's a one-time payment for a lifetime upgrade.
The Shodan Membership is a lifetime upgrade which doesn't expire. If you know you bought it and aren't seeing it on your account then you were logged-in to a different account (ex. the Google social login) and the membership is attached to that other account. Shodan does not automatically remove, expire or otherwise delete memberships.
Note that Shodan treats social login accounts as separate Shodan accounts - even if they share the same email address.
Redeem the gift from within your account settings by visiting the following URL:
https://account.shodan.io/gift
Yes, we provide free upgrades to students, professors or IT staff at universities. If you create a Shodan account with your academic email address then you will automatically receive the free upgrade. If you don't receive the upgrade please email academic@shodan.io from the same email you used to sign-up.