Are all other apps that can use the networking connection turned off? With many of the various iPad console control apps allowing email, Safari, etc. to poll will result in dropped connections.
Except that doesn't explain it losing connection when docked. I have 4 iPad 1's at my work still and we have intermittent issues with them doing much more than even check in, and credit card processing. I've retired them from Crestron/wireless mixing control.
Being that they can only go up to iOS5 I attribute that to the problems I'm experiencing. I don't really expect software developers to maintain their software to work on 3 different iOS versions, as I know how difficult it is with desktop programs.