I'll decline if they're very rude or let their clock run for 10 minutes... stuff like this.
I'll decline if we've already played many games and one of us has been doing much better for many games in a row.
I'll decline if I don't have time for another game.
Other than that, I'll accept.
Some people do get emotional though. If it's a "lucky" win sometimes I'm nervous after I accept my rematch But mostly I think they really want to win so they might get sloppy, so I count it as an emotional edge >:-)
I think for some people it's too much emotion. They want a nice anonymous game where they don't have to think about anything but the game in front of them. So I say don't take it personally if they decline, there are plenty more opponents, best to just ignore and move on.
I know there's a few here who do this and I would just like to say, why decline a rematch?
For sure, if you lose a game you want a rematch. If you win, they'd like a rematch. I never ever decline the rematch. I've played rounds where I've got demolished the first game and then won every game there after. Similarly, I've won the first game then been offered a rematch then lost poorly.
I'm highly suspicious the decline is to do with their rating and the possiblity of losing the points they just earned. Seriously, in the long run does it even matter?