Is there any limit to the number of times a day I can stretch my back to try & eliminate a constant stiff back & back pain? Is more better?

No. There is no limit. Doing more does not make it better. just do not do it even though it hurts. Avoid activities that hurts your back.
No. No, there is no limit. However, if you continue to need to do this in order to have relief of back stiffness, I would recommend you see your doctor for evaluation.