up and down the steps

Hello,
We were wondering if (Parson) JRTs are prone to back problems? (Previously I had owned a terrier/beagle mix who suffered from some back pain which usually occurred in damp weather. Our vet told us that beagles, dachsunds (obviously) often suffered from this type of back problem.) And, I would assume that the puddin' JRTs would be likely candidates for back problems too.

The reason I ask, is that our JRT runs up and down the steps in our house constantly. I try to limit his access to the stairs, as they are really steep, but it seems that it must be really hard on his back. He (like every other JRT) is also jumping constantly, so I just wondered if the stairs might provoke an injury? Thanks for your time.