Airport Extreme help!

My Airport Extreme, which is extended from a BT home hub 4 keeps dropping out of signal

Unless your AirPort Extreme is connected to the BT Home Hub by Ethernet it is most likely NOT actually extending the BT's wireless network. That is because the two are incompatible for this feature.

Ok, thanks for clarifying that for me. You have the basics for a roaming network.

Roaming Network Setup Basics

• Setup the BT Home Hub, connected to the Internet modem, as a router. That is, it must have both DHCP and NAT enabled.
• Setup the AirPort Extreme base station as a bridge. Network tab > Router Mode: Off (Bridge Mode)
• For each base station:
• Connect to the same subnet of the Ethernet network.
• Provide a unique Base Station Name.
• The Network Name (SSID) should be identical.
• If using security, use the same security type (WEP, WPA, etc.) and password. Note: It is highly recommended that you use WPA2 Personal for best bandwidth performance.
• Make sure that the channel is set at least three channels apart from the next base station to prevent Wi-Fi interference.

The following are the basic setup steps:

• Power all the base stations down.
• Perform a "factory default" reset on each of the AirPort Extreme base station. Note: You may have to perform this more than once to make sure they "stick."
• Connect one Ethernet cable between the Ethernet port on the BT Home Hub to the WAN (circle of dots) portt on the Extreme.
• Power up just the BT Home Hub. Allow it to initialize. Verify that you can get Internet connectivity with network clients either by wireless or by wire connections to the BT Home Hub.
• Power up the AirPort Extreme base station. Use the AirPort Utility to select it.
• Configure the Extreme with the Network Mode option set to: Create a wireless network. (Note: Do NOT set it to "Extend a wireless network."
• Set the Wireless Network Name, Wireless Security, & Wireless Password options to be exactly the same as that used for the BT Home Hub.
• Set the Router Mode to: Off (Bridge Mode).
• Select Update and allow the Extreme to restart.
• Once restarted verify that you can roam with a wireless laptop or iOS device between base stations and still gain Internet access.