I've checked with two cruise lines, Carnival and Disney, and they are saying that the day of last-minute cruises is no more. Their revenue models are to offer lower prices and more incentives (e.g., tips included, onboard spending credits) early on, but the prices increase as the supply of cabins decreases. (Supply and demand at work!)
The Carnival agent had been with them for seven years, and she said that she able to travel for free whenever there was space available. She hasn't been able to cruise, as there hasn't been space for some time. The deep discounts on the day of travel have not been available since 9/11. And the government has "encouraged" the cruise lines to register passengers early so they can scrutinize your travel information.
Carnival offers some incentives for booking about a month out, called "Pack and Go." But these are often not available for peak season, such as the Caribbean in the summer.
It's interesting that on the Carnival web site, they offer low-price guarantees in case they offer a lower fare after you book. Their revenue model is such that prices will rarely drop.
The Disney agent said that their ships travel with 100% occupancy. So booking on the days immediately preceding departure would incur the highest cost.