What happens when high blood pressure won't go down even when taking medication?

Depends: What med(s) are you on? Are you at maximum dose of each? How high is the blood pressure? Are you overweight? Are you diabetic? Docs have a number of different BP meds that work by different mechanisms; so they can change meds, increase doses, add another med. Exercise & eat healthful meals to attain proper weight & relieve stress.

BP hi on meds: You have what is called drug resistant HTN. Often do to a specific cause. Most can be easily tested for. That is what I do and happy to help.