Differentiate yourself from your competitors by trying harder. Offer some way to make your customers' lives easier if they buy from you. Don't quit so soon. Ask questions to overcome objections and don't shy away from a little assertion. Think about what they could do to take business away from you, and then carry out that action yourself.
Customers buy solutions to their problems.
To make your product more valuable to your prospects, align yourself with their needs. Review in your own mind if there's something you're able to give so the customer can gain more of a win. This shouldn't involve price concessions. It could be promises of service attention or additional information. The idea to remember is that some customers are demanding because they think that's the way to get what they want.