Hello, my name is***** and I'm happy to help answer your question about Sampson. Boston Terriers are one of my favorite breeds! I'm sorry to hear he is having trouble with balancing and knuckling over in the forelimbs. I'm glad you had him evaluated by your veterinarian. I have prepared some information on neurologic disease below.
Based on your description of his signs, it sounds like your vet was on the right track when they mentioned back or neck pain. Boston Terriers are predisposed to something called Intervertebral Disc Disease (IVDD), which is similar to a slipped disc in humans. In between each vertebrae there lies a cartilaginous disc which I think of as a jelly donut. Over time those discs can degenerate (like an old, dry, jelly donut) and then with normal activity (jumping down off the couch, for example) the jelly inside the donut can be squished out and pushes on the spinal cord at that level. This compression of the spinal cord results in weakness, incoordination, severe pain, and can progress all the way to paralysis of one or more limbs.
Generally we first attempt medical management of presumed IVDD by giving pain mediation and anti-inflammatory drugs (prednisone), as your vet did. However the most important part of medical management, is STRICT CAGE REST. Cage rest (meaning that he is confined to a kennel 24 hours a day except for short potty breaks outside) allows the body to lay down scar tissue over the site of disc herniation. If we don't cage rest these animals, then the jelly part of the donut can squeeze out more material and their signs can worsen. Cage rest is generally continued for a period of 2-4 weeks from initial onset of signs.
If a dog fails to respond to cage rest and medications, or if their signs worsen despite resting, then we recommend advanced imaging (CT or MRI) to identify the site and cause of the neurologic disease. If it is confirmed to be a disc herniation, then we take them to surgery to decompress the spinal column and to remove as much of the disc material (jelly) as possible.
Aside from IVDD there are a few other possible causes of his signs. He could have an inflammatory disease (meningitis) of his spinal cord, which can be infectious or non-infectious. He could have an infection along the bones of the spine, or he could have a tumor growing in the region of the spine that is causing compression of the spinal cord. The only way to differentiate between all of these is with advanced diagnostics (imaging, spinal tap).
Please let me know if this answers your question or if you have any further questions regarding Sampson!