As Mac OS X only has one Menu Bar and almost all applications use that Menu Bar, you will only be able to see the menus of the active application. As Safari is selected, you will still be able to see the Skype window, if it is not hidden behind another window (Safari or Finder or ...), but you have to click the Skype window (or change to Skype via CMD+TAB or clicking the Dock icon or using Exposé via the F3 key) to see its menus.
Or can you be more elaborative what actually happens? Do you experience application shutdowns when you open other applications?
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