https://www.amazon.com/gp/help/customer/display.html?nodeId=...
"If you received free shipping through Amazon Prime, you may be eligible for a free one-month extension when the promised delivery date isn't met. Prime Extensions are limited to one per free trial and 12 for an annual membership. Free Amazon Student Memberships do not qualify for this extension."
Just contact support about that order and tell them the item didn't arrive in time and you'd like your free month of Prime. Since they switched to the Amazon delivery service I'm about to max out my 12 free months.