I am wondering why my opponents time runs down to 1 minute, and then it goes to "A few minutes" and its been that way for the past 10 minutes?  Not complaining, just wondering why we are allowed a certain amout of time per move, but then you are given more time when you should have run out of time. 

Thank You in advance.

I am not sure exactly what the metric is, but it seems that in live games that exceed a certain number of moves, a certain amount of time is added for each additional move. So in quick games that are often won or lost on time, there is an adjustment made for games involving more moves than usual so that interesting games in which there was a reasonable chance to have it decided by strategy would not end prematurely. I do not usually play live games, but you may be able to adjust your settings if you want to play without such an adjustment. There are also cases in which time is added to make up for a calculated lag time based on where the respective signals are going to from each players computer to the main chess.com computer in California. So if one person lived in California and had a 1/2 second lag, and another person lived across the planet and had a 1 second lag, then an adjustment would be made to account for this so that the true time would be the same for both players.