It is persistent (from 11:30am CET this morning, up to now, "still counting...")
The Fedex Delivery Provider is indeed set as "User Server: Live". The "Test Connection" link replies "OK".
Using the same credentials on the Fedex Web Site is said to properly calculate pricing, so I assume the account is valid.
I could not immediately make a test in "Test" mode (the credentials for the "Live" mode are said to be the wrong ones, as soon as you switch in "Test" mode; I'll ask the customer tomorrow morning).
Thanks for helping! Anyway, my post was more a Poll; as nobody else seems to experience the same problem for more than 9 hours now, I assume it may be a local issue.