Given that your Galaxy S7 and AT&T Primetime Tablet have Wifi connectivity within the coverage area of your modem and router but will not connect upon re-entering this region from beyond its limits, authentication is not occurring at the point of re-entry. You can configure your mobile devices to automatically authenticate with the router upon entering its Wifi zone. It is important to note the need to access external Wifi networks with mobile devices using their credentials if permitted if you need to connect to other Wifi networks with them. Also, when using your Galaxy S7 as a cell phone, Wifi should be turned off.
I currently use AT&T U-Verse with an ISP-supplied router (Pace Model 5268AC FXN) and neither of my wireless devices, Samsung Galaxy S7 & AT&T Primetime Tablet, can connect to it unless I turn the router off and back on again. Unfortunately, that's not a permanent fix. If I leave the wi-fi coverage area and come back, my phone will show an authentication error and my tablet will just say that the network is "saved", but won't connect. My laptop seems to connect just fine (my PC is hard-wired) and my DVD players are hit-or-miss. I have no problems connecting to a hotspot or to a friend's wifi. I'm sure it's something in my router, but when I log into it, I don't even know where to begin, much less go. It claims to be up to date firmware-wise.

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