Is there a fix?
That usually happens, when Flickr is looking for newly published albums and the server is unreachable.
I'd recommend to disable the option "Automatically check for newly published albums"
in the Aperture Preferences > Web panel for your Flickr account.
Then you will only try to connect to Flickr, when you select your Flickr set in the Aperture Library and you should see the error less frequently.
If Aperture hangs, try to quit without force quitting, if possible; see:
If you had to force quit, repair the Aperture Library. Force quitting may leave the library in a inconsistant state and cause all kinds of trouble later.
+1 from me.
Totally annoying (especially if your wifi at home likes to disconnect) and it should be super easy to fix such bugs.
Btw.: if you keep hitting cmd+q and enter, you can get Aperture to quit normally. You won't get rid of the error message without closing Aperture though, but it still might be better than force quitting.