I installed Thunderbird 3.1 from Ubuntuzilla packages a few minutes ago and lost the icon in Docky. I wasn’t so happy with that, so I checked around to find a solution.
The reason appears to be that the system is looking for /usr/share/applications/thunderbird.desktop whereas Ubuntuzilla creates a file called /usr/share/applications/Mozilla Build of Thunderbird.desktop; this is not right.
Just rename the culprit file to thunderbird.desktop and you’ll be a happy bunny as me.
That might not be the best solution ever, but it seems to work pretty well so far.