The original bug got closed:
It seems the config disallows the reporter to re-open, so I'm forced to open a new issue.
I believe the root of all evil is the way Mumble implements the systray icon; it's not "persistent". For example, when doing a "killall plasma-desktop" and then starting plasma-desktop again, all systray icons from all other application re-appear on the systray. Except for Mumble's! I suspect this is also the cause of the original bug.
Below follows the text from the original bug:
When I minimize Mumble to the KDE system tray, a single click on the tray icon is more often than not not enough to restore Mumble again. Usually, a single click only works when performing it immediately after having minimized the window. If I interact with other windows first, then anything between 2 or 4 clicks (usually 3) is needed to get the window restored. When this happens, on the first click the Window appears for a fraction of a second and then disappears again. After keeping clicking it, it eventually appears.
This bug was there since the first time I ever used Mumble, which was 1.2.0 beta1.
Sound system: ALSA
Gentoo Linux AMD64
Linux kernel 2.6.35/36
KDE 4.4.0 to 4.5.2
Sound card: SoundBlaster Live 24-bit