I think I know what's causing this problem but unfortunately do not know a nice way to solve it...

It's probably caused by something like this:
When the tab bar starts getting filled up to the point where it *almost* fits the top region, but still
doesn't, the tabs resize to fit it. At the same time the arrowscrollbox element kicks in and starts
showing those arrows at the right and left hand sides of the bar. These two actions collide, with the
tabs resizing and the arrows displaying/hiding, causing infinite flickering until the user does something
about it, such as e.g. closing a tab or opening more tabs.

As I said, I don't know any specific solution to this problem without having it go thorough testing as
the bug doesn't always reproduce easily. It could be the CSS, it could be the combination of the two
types of elements and their normal behavior. Either way, I think we're probably better off if we migrate
from tab-bar.js to new-tabs.js as we have some big plans for the latter, with high customizability, etc.
After all, new-tabs.js was based on tab-bar.js...