For what ever reason none of my Samsung S4's will stay connected to my verizon router.
It works fine with all other routers...
As long as I keep doing things on the phone it will stay connected, but if I set the phone down for more than 5 minutes the internet will stop working.... I have to disconnect it and reconnect it.
The S4 device works fine with all other routers, tested with neighbors and girlfriends att router.
Currently no firmware updates for either device (router or phone).
Are you all running Android 4.3 on your Galaxy S4 devices? That was released a few weeks ago and from what I understand, addresses some of the Wi-Fi issues that were seen out of the box with the phone. Also, make sure you don't have some battery saving or task killing app installed that is actually shutting off your Wi-Fi.