Hi,
Thanks to the input offered by both:
Vincent Maverick Durano, and
ZurdoDev, I found the root of the problem!
It was a div tag inside an updatepanel (Vicent, you are right, they are "Evil"), which simply decided to ignore the Update() method being invoked from code.
divClickOut.Visible = false;
UpdPnlBackDrop.Update();
Since the div is transparent a has not effect on tab, etc. key-navigation, its presence was not obvious.
On the other hand, as ZurdoDev suggested, I did use the browser's debug tool (again), to inspect scripts, html, etc, but overlooked the simple, yet effective
right-click => "Inspect Element" option.
These ideas allowed me to detect the problem of this "odd behavior"; now, I'll get on fixing it.
Thank you guys.