We also own a business and have just recently (within the last month)stopped offering our online customers the option of using their AMEX. We have yet to see any difference in our sales. I do want to point out that if they call and inquire about using a corporate AMEX, we will take it...our walk in customers and long time account still have the option. Mostly we are trying to get away from the online customers who buy 20 dollars here, 50 dollars there from using their card that costs us, the company, more in the long run from all their silly fees.
As for restraunts, I see no reason why I would pick one place over another because they take my AMEX. I love the card for various reasons, but I have no problem paying with our corporate MC if they prefer not to deal with AMEX. I will always look to see if they take it but if not...no big deal.