As some have pointed out, with a timeout and possibly icings, there's a good chance to have your top players out there for most of the last 2-3 minutes. The optimal time to pull the goalie probably depends on a number of factors, such as composition of both teams, but I think it's much earlier than 1 minute left.
Too often, the trailing team doesn't even get much of an opportunity in the last minute. If the team is trailing with under 3 minutes and establishes possession in the opponent's zone (with some of its better offensive players), I wouldn't hesitate to pull the goalie. It's very, very likely you will have to pull the goalie at some point... why not when you have clear possession and any penalty incurred as a result of the extra skater will result in a power play that can be fully utilized.
Otherwise, all the opponent needs to do in the final minute is gain possession... or make a couple of clears... or even take a last minute penalty, and the game is basically over.