STEP 1. Simply relaunch Mac App Store.
STEP 2. From the ‘Store’ menu, simply click on logout button to logout of the Mac App Store and again log back in by re-entering your credentials. Now you should connect as usual.
That’s it. In this way you can fix “Cannot Connect to App Store” error message in Mac App Store. You should note that when Mac App Store is down at this time you may get “Cannot Connect to App Store” error message.