I have dsl running ppoe and router set for 2 iPads. I set router for "stay connected". But when iPad cover is closed for a minute, I'm forced to choose a network again when I open the iPad and go to Internet. Is there a setting that would allow continuous network connection even after reopening the iPad?

I'm pretty sure your router's 'stay connected' setting refers to it's connection to the sever, not your iPad's connection to it. They should be unrelated.

Unfortunately some routers and the ipad just do not get along. Sometimes you can adjust it to work properly, but it's so specific to each router that usually, after a lot of messing around, most people choose to just get a newer router. You can always contact your provider (if they supplied the router) or the manufacturer to see if they have a fix.

But there are a few things worth trying first. This more or less combines them all into one.

Shut off your router.

On the iPad, go into Settings >> General >> Reset, and choose Reset Network Settings.

Restart your iPad. Hold down the power button until the red power off slider appears and slide it off. After the iPad shuts down, hold down the power button again until you see the Apple logo.

Turn on your router and wait for it to finish rebooting.

If the iPad does not ask if you want to join the network, after the router reboots, go to Settings >> Wi-Fi and manually join your network.

Test to see if it works properly now, and continue to monitor over the next few weeks to make sure the problem does not reappear, at lest not too often.