Or, you know, you could get physical therapy. I had chronic back pain as a result of my job as a programmer and the only way I was able to fix it was to go to a good physical therapist and actually follow through on the physical therapy. My pain was a result of a number of muscle imbalances and posture issues and it took a few months of every-day work to fix the problem.

I suspect that the OP has a specific muscle imbalance that archery just happened to target well. But it's unlikely that this broad recommendation is going to work for everyone with back pain as the causes are myriad.