Exercise not helping back pain despite engaging in a regular strength building program and having a strong back.
Exercising, although essential for a healthy lower back and prevention of injuries, doesn't necessarily equate to not having or getting lower back pain, or the ultimate cure for lower back pain.
Many, many world class athletes, all in the prime of their careers, usually at their best fitness level, having strong backs and nearly as strong as they will ever be, still suffer with lower back pain.
A weak or unfit back doesn't necessarily mean that is the cause of your lower back pain. The flip side is true as well, even if you have lower back pain that doesn't mean your back is weak.
There are many causes of lower back pain. Having a weak lower back isn't one of them. Having a weak lower back will predispose you to back injury that will cause lower back pain. But... by itself it has little to do with pain.
There are many people who have very weak lower back muscles yet they have no lower back pain.
You can have strong lower back muscles, but perhaps you have DDD causing a facet syndrome. Keeping your back strong may help to prevent further trauma, stabilize your lower back or halt the progression of the degeneration. But it won't cure your DDD or facet syndrome and the pain associated with it.
It is just one piece of the overall puzzle of building the best lower back in order to manage your primary back pain diagnosis.
So, despite exercising you will probably still have lower back pain until you identify, treat or correct all possible causing and contributing factors. Such as:
Yes, exercise is important. But by itself it will not cure your lower back pain.