I understand about compression waves, but I think that the softness of barrel steel isn't going to retain energy very well beyond a few cycles. I wish I had enough engineering skill to calculate the energy retention of steel through a vibration cycle to prove/disprove that thought.
To get back to the tuning fork analogy, the frequency doesn't change with time but the amplitude does. No matter how you ring it the "natural frequency" will come out, but the volume (amplitude) will depend on the initial input of energy. But you can see how the quickly amplitude can decrease.