At Merchant level 3 in Recettear, you gain the ability to give customers sales recommendations. However, I've had some customers come in asking for a type of item that I do not have in stock at the moment, meaning they leave without a purchase at all. Does this have a negative effect on the relationship I have with them, and if so, is it easily made up for with later sales?
No you don't, You only lose approval by not making a sale, or not buying an item from a customer.
Although I'm not sure if it will get rid of your bonus exp per sale though, but that may be the only repercussion if that even happens.