If you change the Sidewise option "When browser toolbar button is clicked" to "toggle sidebar on/off", does that give you the behavior you want?

Not the highest on the priority list, but this is also something I would like to see in the future.

Chrome does have a facility for capturing "webpage thumbnails" of each tab, though the user must first view the tab in question before this can be performed. As such I'm not sure if having only "some" thumbnails show up would inhibit this from being a really valuable/reliable feature. 

Thanks for the info. I don't know what would cause those buttons to disappear but I'll keep an eye out for it. I'm also currently working on addressing the "stuff disappearing" issue.

I really want to get this problem fixed but it is a difficult one to reproduce. So far I almost never see it occur here, and can't reproduce it reliably.

I'm going to try some new methods of "forcibly" causing Sidewise to do this bad tab-jumping behavior this week to see if I can trace down the exact cause and/or appropriate solution.

Can you enable diagnostic logging in Sidewise options, then once you see SW pegging the CPU, go back into options and click 'Send diagnostic report'?

That may give me enough info to reveal what is going awry here.