This sounds like some of the problems others have had with the WiFi. Do you have your home network saved in settings. If not you should save it. Whenever you connect to a different network (coffee shop, panera, starbucks) you can go into settings and save that connection. That should help. If this does not work you may need to take your ipad to apple and have a genius help you.
I am wondering if you a dropping the connection because of the encryption or because of another issue. My advice to see what the problem is would be to temporarily disable the encryption on your router and see if you get dropped connections.
Also, if you want a second way to secure your wifi is to use mac filtering ... It's a bit more technical than using keys and passwords, but I use it and it works fine ... Of course many balk when they realize each guest or new device needs it mac address to be entered on the router.
My experience is the same as gentlefury's. I have used my iPad on multiple networks and have only had to enter my info the first time I used the network (just like my iPhone). If I had to re-enter my password every 30 minutes, I would get a replacement from Apple.