How to correct an Authentication Required popup when connecting a cell phone to a wifi network?

So, long story. My dad asked me to fix wifi on his Samsung Galaxy S3 Mini. He would turn off wifi when leaving the house so it wouldn't drain his battery and then turn it back on when he got home. I wasn't having issues with my iPhone 6 until I turned off my wifi and then reconnected. Our wireless network shows up and the devices can connect to it. But afterward, especially when trying to access a browser or use an App that connects to the internet, an Authentication Required popup would appear asking for a user name and password. The router is a Belkin N600 N+ and is connected to a Windows 10 HP desktop through an ethernet connection. There are no wifi problems on his older desktop, which is in a separate room from the one that contains the router. I have tried resetting our router, changing settings on the router, restarting both the router and the modem, changing network settings on the computer, updating network adapter drivers. Our phones will stay connected to wifi for a while and then the Authentication popup appears and we can no longer use wifi. Nothing seems to work for long. Please help.
Added (1). We are not connected to the guest network, there aren't duplicates of the main network, and I've had both cell phones forget the main network multiple times.

Read more: How to correct an Authentication Required popup when connecting a cell phone to a wifi network?