Hi Roi,
I must agree with Dave here, that this is not a typical functionality of a Web application, and the expected behaviour of a double click within a TextBox is exactly what James describes in his message.
As you did mention it, yes, the original problem was reported back in 2008, and still has a research status. Some results have since appeared in linked reports which have revealed the real nature of the problem and we now know that the actual reason for the problem is that the ValueChange event on the TextBox is fired after the Click (or somilar events) and by the time your serverside starts processing the Click event, the server-side value of the TextBox hasn't been updated.
This is a general infrastructural problem that affects more controls that just the TextBox, although it's most obvious for the TextBox. Fixing it generally, however, is not as simple as it may sound, and will most likely require quite many changes to the core which will have major destabilizing effects on the framework which we do not want to risk for a stabilization release. The schedule is therefore set to the next available release, the 6.4.1 version.
Palli