The version just updated is
11.8.800.97. During the installation, the installer requires me to close Skype. Does the 2 software have any relationship ?
Note: I'm using Mac OS X 10.7.5
It's common practice for upgrade installers to check to see what processes have opened files to the software being upgraded, and alert the user to any instances where applications may become unstable or lose data if a software component is modified while in use.
How exactly Skype is using Flash Player, I can only guess, but I've confirmed that Skype does indeed use the plugin, and so quitting Skype in order to let a Flash Player software upgrade proceed is necessary.