I spoke to the Sprint Rebate Center, and this is what they said about the "Phone Upgrade Rebate."

If you've have the same phone for more than 18months, you qualify for the rebate, regardless of how much time is left on your contract. HOwever, in order to get the rebate, you ALSO have to renew your contract. Renewing for 1 year gets you a $100 rebate, renewing for 2 yrs gets you $150.

So, the phone upgrade rebate DOES require you to renew your contract too. It's not just the 18 month thing.