The most blessed thing that can happen to a company in regards to the customer service is just having such customers. He has been with your company for a long time; he has been there during your ups and downs. He knows the strengths and weaknesses of the product. He is willing to forgive your weaknesses, and he praises your strengths to the colleagues and friends. Over the years, you have built warm relations.
What to do: never leave these customers unattended. Do not reject to give a discount saying you cannot do this. First, find out why all of sudden he has asked for a discount. As soon as you know the reasons, it becomes clear how to react. If they are expanding their business and now they need to buy more from you, then agree to discounted prices and work on other options to propose the better prices. The customer will appreciate it, he will bring friends. In case the customer's budget was reduced for some reasons, he just cannot allow the products for the current price, then look for an offer that the customer can accept, otherwise, you may lose the customer. Another case, the customer just realized that he deserves a discount given a long-lasting partnership, then weigh all the pros and cons. In practice, it has shown that in this scenario the customer stays with you regardless of the discount. Such request for the discount is more like a "wish" rather than a "necessity".
If you offer a discount to such customer, the level of loyalty will grow, and later you will be justified to have tiny mistakes (malfunctions, bugs, overlays and other). More precisely, there will be a limited amount of errors that are guaranteed to be forgiven.
In brief: investigate the details related to the customer, figure out his motivation and a payment history. Do not be afraid to lose money but be afraid to lose the customer.