@RouterRob 

In terms of the internet usage on your wife's phone, some useful information regrading how to prevent this from happening can be found here: 

Block Websites From Using Up Internet Time

Let me know if there are any other workarounds that you find or think of for the topic.

Now onto the Tether app, my first thought is that your wife is being logged out of the app due to some sort of security conflict.

When your wife is logged out of the application, are you also using the same account on one of your devices?

Have you tried seeing if the problem persists across another device, such as a Tablet?

Another thing that may be causing this would be the security features on the phone itself. Many modern phones will allow you to connect to a network using a private MAC address; I would see if this setting is different from the settings on your phone. This setting would also influence the Internet Usage Time as the router would not be able to effectively track the device.

Lastly, a quick recommendation that could be tried, is to assign your wife's phone a static IP address from the app and see if she is still periodically logged out.

The best thing that can be done in this situation is figuring out what factors contributed to or what conditions led up to the time when your wife's phone was logged out. If you have some more detail, feel free to let me know, and we can try to work out what is causing it.