If you can't connect to the App Store, iTunes Store, or other Apple services https://support.apple.com/en-us/HT201400. There have been quite a few Apple server connection problems lately. Among other things, in the above document, see Check Apple’s System Status page. You can check there to see if the needed server is available when you need to use one.
Also, below are the alert messages given in the document. But, receiving others is a possibility. Use the steps in the above document if you see one of these error messages or a somewhat similar message.
· "Cannot connect to the iTunes Store. An unknown error has occurred."
· "We could not complete your iTunes Store request. The iTunes Store is temporarily unavailable. Please try again later."
· "Could not connect to the iTunes Store. Make sure your network connection is active and try again."
· "We could not complete your iTunes Store request. The network connection could not be established. There was an error in the iTunes Store. Please try again later."
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Also see these search results error connecting to the Apple ID server. You will see a number of links that are, or may be, related to your specific problem. I have not see a definitive fix though. The results related to "verification failed" may be closely related to your problem.