See that doesn't make sense to me. You say you use high tracking sensitivity so you can recover more quickly when getting back on target after losing focus but the whole point of setting a lower tracking sensitivity, as Case 2 originally does as standard, is to stop this happening in the first place, so if the target strays from your selected AF points momentarily, the AF system won't immediately focus on the background.
Or is it to do with the length of time you lose tracking on the subject? I guess the low tracking sensitivity is intended to deal with momentary losses of tracking on the subject or interruptions such as something moving between the camera and subject. Even with low sensitivity, if tracking is lost for any length of time, I guess the camera would give up and refocus on the background, at which point you'd want high sensitivity to bring it back to the bird as soon as possible?
I'm guessing here of course as I'm not a bird photograher by any means. Whilst I've used Servo AF quite extensively, I've never shot anything as erratic as BIF