Hey there @alyssakasher and welcome to the community!
The verbiage in the contract varies by country, but here's a snippet from the USA student site:
Qualifying Students are entitled to receive a discount of fifty (50) percent on the monthly subscription price of the Spotify Premium Service (as defined in the Spotify Terms and Conditions of Use) for each month (the “Discounted Month”) up to a period of twelve (12) consecutive months ("Discount Period").
Basically, you can re-sign up, but you have to do it every 12 months. There's a cap of 3x. Hope that helps!