Just to be sure I understand. You take your laptop with you but leave the AirPort Express ... correct? When disconnecting the laptop from the Express the Express' status LED switches from solid green to either blinking amber or solid amber ... correct?
Is the Express the only router in your current network configuration? That is, is it connected directly by Ethernet to an Internet modem or to another router upstream of it? If either what is the make & model of this device?