Well, this made sense to me:
I can't see any reason why Microsoft would restrict the amount of email addresses from a particular provider.
And so did this:
It finally turned out to be a misspelling in the Outgoing and incoming server info. I hope it's that simple for you to fix.
So, despite what the BT people told me, I took a deep breath and copied the settings of the BT mail address I'm currently using on the phone - though I swear I did this during the weekend - and spelled everything very carefully - though I swear I did this during the weekend... and the second address synced straight away. So it could have been operator error on my part, or BT's servers hanging during the weekend, or something else. Anyway, grateful for all your help and that it's resolved. Case closed.