I am also with BT and have had the same problem with WLM and it's logon box. I've finally got mine working properly again.
How many email accounts are you pulling in? I am using three. BT, Live and Gmail.
With BT set as my default account I went to Account Properties and under the General tab I ticked the box "Include this account......etc". Apply.
Touch wood, the login box has not reappeared.
Hope this works for you.