I was trying to figure out a way to prepay Dropbox for another couple years to take advantage of my Amex 40% offers on 2 different Amex cards. My plan auto renewed right before the offer appeared. Unfortunately there doesn't seem to be a way to do this.
However, on a whim, I clicked "cancel plan" at the bottom of the "Plan" tab in my account settings. I was immediately offered a 20% refund of this year's subscription fee if I stayed on board, making my total cost that of last year's (before the price hike).
Hope this helps someone. YMMV