iPad 'not auto-connecting' solved!
Long version: My iPad started the 'no auto-connecting' problems this morning after 3 days of perfect use. I was using settings specified in http://support.apple.com/kb/TS3304 and my network was working fine for other devices. I tried rebooting, forgetting network settings, and resetting my router, but nothing worked. Every time I woke the iPad up from sleep, I had to go into the wifi settings to reselect my network (though, it did retain the key).
I was looking at some pictures a few minutes ago and realized the screen was very dim and remembered that I set it to minimum brightness last night. I turn the brightness up and didn't think much of it. After a few minutes, I picked up the iPad again after it had gone to sleep and for the first time today, it immediately had a network connection.
The problem is repeatable - after I turned down the brightness to the minimum setting again and let it go to sleep - no network. Turning the brightness up a little - network retained after sleep.
In fact, when I turn the brightness to the minimum setting and let the iPad sleep, it wakes up with no network. If I increase the brightness, it immediately reestablishes the network connection as soon as I move the brightness slider - I don't even have to go into the wifi settings to re-choose my network. I don't know if this is a bug, or an undocumented power-saving feature for low-power night reading, but I'm happy with my iPad again.
iPad 16gig