When devices reconnect to Airport, no internet connection

I recently purchased an Airport Express directly from Apple. The setup was relatively easy, everything connected fine. I do have an error message that says I do not have a valid IP address, but my connection is fine, so I've ignored the message.

When any household device (one MBP, two iPads, two iPhones) leave the house and return, each will automatically reconnect to the Airport (as it should and as it did with my previous router), but there's no internet connectivity on the device that left the area. All other devices that have NOT left the area are fine with a normal connection.

If I turn off wi-fi on the device, then turn it back in immediately - the wi-fi connection is reestablished and I have functioning internet connectivity.

Somewhat of a minor inconvenience, but growing quite annoying to do EVERY time I leave the area and come home.