Known bug - supposedly a patch is on the way. This is hazy, so you might want to do a search, but the recommended fixes are to disable "autosensing" in brightness and use WAP security rather than WEP.
After the first week, I signed up for AT&T's $29.99 unlimited plan because Wi-Fi was so slow and limited in range. My iPad has about half the range of my Gateway Vista laptop.
I don't get a pop asking for my password but I do get a pop up saying Network lost and asks me to dismiss or check the settings. Not very often though.
I was having issues with this as well. I moved my wireless router to the other side of the room and it works much better now. The range on these things is not very good.