Human players have option of saying no, try playing a computer it never say no and they make nice loser, they always say good game when they lose and never refuse a rematch.
Are you supposed to accept a rematch offer on live chess?

You should always decline a rematch. It's just a computer taking over disguised as your current opponent.

Just always ask yourself "what would Jesus do?"
Wise words to live by. However, I don't think Jesus would have a problem as to declining a rematch if he didn't want to play anymore.
Therefore, I think you can still decline the request.

Actually, it's bad form to give a rematch. What if you win? You will then be up 2-0 and how do you think your opponent will feel about it? Bad, that's how! Do you want your opponent to feel bad? OK, then declining is far the best policy. So, that's settled then.
It seems to me that the OP answered his own question. Furthermore, he tells us he has been on the site for three years. If so, he surely cannot be unaware that this subject has been exhaustively and repeatedly thrashed out many times before.

It seems to me that the OP answered his own question. Furthermore, he tells us he has been on the site for three years. If so, he surely cannot be unaware that this subject has been exhaustively and repeatedly thrashed out many times before.
of course he knew that, he just loved the attention.

You should always decline a rematch. It's just a computer taking over disguised as your current opponent.
Yeah... that's why i hardly win a rematch. Never knew mad men gone mad could be this wise.....

Actually, it's bad form to give a rematch. What if you win? You will then be up 2-0 and how do you think your opponent will feel about it? Bad, that's how! Do you want your opponent to feel bad? OK, then declining is far the best policy. So, that's settled then.
Clearly, if they ask for a rematch, then they obviously want to play. and what if it's a draw? What if you lose? then it woll be 1.5-0.5 or 1-1. You can decline or you can accept.

I sometimes like playing the same opponent a number of times (especially if they're finding ways to crush me!) because I slowly learn how to respond to their ideas, and I feel it makes me a better player.
Sometimes I don't have time to play more than 1-2 games, which is fine! You can do whatever you'd like :)

You are living in a free country...cops are not going to chase you for accepting or declining a rematch request

Suffer the little chess players to come unto me, Jesus said.
Nice pun on Matthew 19:14! :)

Bless you my pun.
You're good with puns! I like puns!
A friend of mine, who really likes puns, told me that, one time, he had thought about wearing a T-shirt with the word ‘puns’ in it. There was just one problem: in Portuguese, the word ‘puns’ means ‘farts’, which might make it extremely awkward to walk with it in our hometown; so he gave up on the idea.
Just always ask yourself "what would Jesus do?"