Thanks, Sylvan, I might try that.
Based on the lack of any other replies to this problem, it is a very rare problem?
I am really afraid that the bladder is shot. But, there is no air in the water or rust or any other problem.
One other detail: I drain and re-fill this tank about 20 times per year because it is in a cabin without freeze protection (heat). Each time it drains, it the pipes/tank make a loud groaning sound. Can that be good? Is that a sign of trouble?