Routers that are dual-band may have trouble with ipad. This is documented in apple's KB. If it is a problem with an apple airport product, apple should definitely be able to help. If it is a problem with a third party router, make sure the router's firmware is up to date. Then contact Apple Support, notify them of the issue, follow any recommended steps, and get a case number with a date.
You have the right to a hardware replacement if you need one.
Questions:
1. Does the network name appear on the list?
2. With a utility similar to istumbler, do one or two bands appear on the list?
In my experience, the channel on your router should be set to "auto". The mode on your router may also needd to be tweaked so that it is using a standard spec (G, N etc.) and not trying to extend the range using proprietary protocols.