Thanks for your response. I never considered this to be a “problem” with your plugin; just a behavior I had to learn to work with!
The entire routine that runs within each tab comes from a plugin I am writing. Each tab has its own shortcode.
I figured that the jQuery/Ajax approach was probably the way I would have to go, but I am not yet familiar with those and have resisted learning. I guess there is no time like the present to learn them!