When you say looses the connection after sitting, this would be normal behavior, unless you qualify that with additional information. When the iPads or iPhones are connected to wi-fi, if that connection is not actively being used downloading, uploading data, when the iPhone goes to sleep and the screen locks, wi-fi will disconnect, to conserve battery. However, once you wake the device, wi-fi should automatically reconnect. If the iPad or iPhone is connected to power, it will remain connected to wi-fi. I'm guessing here, but it seems that it may not be reconnecting when you wake it, is that correct?
In your second paragraph you mention many of the standard troubleshooting steps except one. Have you restarted your router? While many will say that since other devices are connecting and working fine, they don't believe it can be a router problem. This is not true. The router does all of the assignments for IP addresses for wireless devices, and can sometimes get stuck on one. Remove power from the router for about 30 seconds. Then plug it back in again and wait for it to reboot and re-establish its connections. After that attempt to reconnect the iPad and see what happens. This information is also included in this support document, If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
If necessary after that, you can make a Genius Bar appointment at the nearest Apple Store for an evaluation.
