Why would a shop refuse card payment if the alternative was no sale?

Its a hangup from the old days when Visa and Mastercard and Amex used to interchange connection fees with processing fees. Small transactions would have a minimum fee so it actually was not worthwhile making small transactions or single transactions. But nowadays the card companies have percentage fees however for convenience stores they operate on the business model of buy cheap as possible and sell for a much as the customer will pay. Margins vary from break even to 50% in extreme cases but at best they average 15% on most lines. Most store owners know their margins on the popular products and drop prices on some products to entice sales. My father in Law's store used to drop the price of things that were getting close to sell by dates to move them. Processing fees cut into that margin. There are some situations where it could be a loss although rare, the store owners aren't there to manage the transactions so a blanket rule prevents having to explain all that to the cashiers. Cashiers don't care they'll just process the transaction cos they just wanna get through the queue so they can get back to looking at reddit. Others follow the rules or sometimes you'll meet the store owner on the till.