@KubaLuka 

The Archer C7 not having internet is the result of the WAN port not receiving internet. The RE650 is connected to the Archer C7s LAN port so that does not seem right.

When the issue happens, log into the Archer C7 and look at the Advanced > Network > Internet menu. See if there is still a public IP address or if its all 0's.

@Tony 

Hi Tony, thank you very much for the quick response. I'll check that out. And what should be the right state of the setup of both devices?

Thank you very much

@KubaLuka 

When looking at the internet menu, note what your IP address is. If the router is losing internet from the modem the IP will display 0.0.0.0.

What you can also do is to set up the extender as a range extender rather then an AP.

@Tony 

And will the range extender mode function over LAN?...so the wifi on the Archer C7 router will be turned off no matter what...and the extender will be connected through LAN to it....So the extender will distribute the wifi only when it gets the electricity from the smart plug while the wi-fi on the Archer C7 will be still turned off? I apologize for so many questions. Thank you for your patience.

@KubaLuka 

The RE650 in extender mode may not be a alternative since you want the Archer C7 Wi-Fi off. A first place to start would be to see what happens to the internet settings when the issue arises.