R8000 HAS Internet and does NOT have Internet at the same time

Any thoughts why this may happen with X6 AC3200 WiFi Router (R8000) 

• On one hand, almost all connected Wi-Fi devices drop Wi-Fi or claim "no Internet"; Anveo monitoring service says "SIP offline".
• On the other hand, router's admin screens (both via Chrome and Android app) claim that Internet is online. 

Here are the details:

Occasionally, I start getting a "No internet" error when I connect to my X6 R8000. When it happens, it happens from all wireless devices at my home -- they drop connection or cannot connect, with an exception of a wireless device (work laptop) that previously established a VPN connection: it stays connected to the Internet until I manually stop the VPN.

Around the same times, I get a "SIP offline alert" email from Anveo.com monitoring service to which I am subscribed.

I can force a Wi-Fi device (such as my phone) to stay connected to the router, and then I can access the router's admin screens via Chrome at routerlogin.net and -- lo and behold! -- it claims that the Internet status is Good(!!!???). But I cannot browse Internet.

I can also access the router's admin screens via my phone's NightHawk Android app (when disabling Wi-Fi on my phone). The app shows that my router's Internet is ONLINE(!!!???). Not only that: I can test the Internet speed from the NightHawk app, and it shows close to expected speeds.  Mind you, there's no Internet on all my Wi-Fi devices at that time.

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I found that if I go to the "Basic Internet Setup" admin screen in Chrome and click the green "Test" button, the router reboots (I think) and then the problem disappears for a while: I regain Internet on all connected Wi-Fi devices. Also, I receive a "SIP recovered alert" email from Anveo.com monitoring service.

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My R8000 has the most up to date Firmware Version 1.0.4.84. 

NightHawk Android app is up to date.