That message just means the device couldn't connect to the play store but the problem could lay from your Wifi connection all the way up the stream to Google.
Do you ever see your Wifi icon turn from blue to grey around the time that problem happens? If you do that is indicating that while you are connected to Wifi, it's not making it through to the Internet. It's normal to see it grey when you intially connect but it should stay blue.
As to why that's happening, no idea without knowing more about how your network and ISP are setup.
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