I appreciate your suggestions. I had already tried most of the ones related directly to the iPad and have since given the others a shot, without success. I have not yet tried any of the ideas around resetting or changing the wifi router.
The most intersting point in all of this is that I did not have any wifi problems with this networkuntil updating the iPad to iOS 5.1.1, and they started almost immediately after the upgrade. Also, I do not have any problems with my iPhone or my laptop. Both the laptop and the iPhone maintain the wifi connection without interruption.
When I get time and start trying some of the router ideas, I hope the issue will be resolved. However, I believe there is something in iOS 5.1.1 that has started all of this, since I did not have any problems on this wifi network before and no other devices in our buiding, including other iPad 2s (not yet on iOS 5.1.1) are having any issues.
I am curious as to whether or not anyone else has had this problem with the new iOS. Next time I will not be so quick to upgrade.