How do you know when to hold the line on pricing and when to lean in and give a discount or concession?

Test it. How strong are they on their price point and are they willing to give in for something else? Also find a bargain and do not give discounts without getting anything in return. Nonetheless sometimes it can be smart to give some discount if you get something in return that is more precious in the future (access to management, other departments, stakeholders, references, ...).