This is because the final few minutes of a contended game are the most strategically complex, as the teams are fighting not just for scoring and control of the ball but also for control of the clock. Usually, the team that's behind is trying to slow down the clock (minimizing time-per-play and maximizing actions that require the clock to stop between plays), while the team that's ahead is trying to run out the clock to seal their win (unless their opponent is likely to score, in which case they may want to slow the clock so they have time to respond, etc). And since the stakes are so high, the teams spend a lot more huddle time to deliberate strategy, as well as going for more complicated or unusual plays that often require more careful review from the refs.

It's by far the most interesting part of the game, but if you're only passively watching and waiting for it to be over, it can feel agonizingly slow.