What does it mean to have intractable back pain?

Difficult to treat: Intractable means difficult or hard to control or deal with. So it doesn't mean impossible to treat, just a challenge!

Pain unrelenting: Pain that just does not go away with simple treatment. Beware of sources of this pain than from the back like an aneurysm, kidney infection or ulcer. An infection of the spine or a tumor involving the spine could also be a cause as well as a large disc herniation.