I have not owned a BT Home Hub, but with one of my Netgear routers, I had a similar problem. It was with an older laptop using win XP, and similar to yourself, I had to re-enter the password which judging by the number of asterisks looked to have changed.
I believe that altering the channel used for wireless on the router improved the situation, and altering the security encryption type improved it further. I cannot remember the exact details, and I am not sure if I ever completely fixed the problem.
I assume it is a fault within Windows XP, perhaps with older hardware. Do you know if your wireless device has a manufacturer program to manage the wireless connection, instead of the Windows wireless connection manager?