What happend to my MATLAB icon on OS X?
Go to info.plist, change LSUIElement value back to 0. This will fix the dock icon. This might introduce some other issues however (I don't use matlab too extensively), so if you experience any visual glitches it might be due to modifying the plist, not matlab itself.

I don't have other machines to verify, but I believe the "issue" you describe is not specific to your machine but is true for all matlab installations on osx, due to Matlab's weird startup sequence. 

The reason why the first launch displays the icon is that the first launch actually launches an activator program, not matlab itself.

Moreover, even after tampering with the lsuielement to restore the dock icon, the alt-tab icon will still be the generic black-rectangle script icon (again due to the way matlab is packaged and launches)