The first question is, does the ereader connect? And can the browser reach the internet?
If it does not connect at all, then the problem is probably that it cannot reach
www.kobo.com. The device fetches a page from there to check if it can connect and if you are using a hotspot. If it fails, the it disconnects from WiFi. If the device cannot see that, then something is blocking it.
Can the Android device running the app reach the internet? If not, you have something else going on in the router.