Because this is our mistake, I would like to offer you a 20% discount on the reservation you made with us.

If you replace 'because' with 'since', does it sound less polite, or the same?

Hi LiJ

I prefer "since" in that sentence simply because the reason being given ("our mistake, not yours") is information that is most likely already known to the listener. I don't think using "because" will actually make it any politer. It seems to me that a "politer" sentence would include some sort of apology rather than a reason.
'Since' does sound comfortable to me, too. 

Thanks, Amy.