What is the best way to consistently strengthen a repeatedly strained back muscle?

Slow and steady. Strengthening the back muscles is a fabulous thing to do! The stronger your back, the less likely to be strained. Backs are tough to strengthen & you need to see a physical therapist or a good trainer for a daily program. Take it slow! Warming up before you do any activity that involves greater use of your back muscles is crucial. No matter how strong your back is, not warming up, causes injuries.