All three worked fine for months, years even, on the same computer. Everything appears identical - all settings and servers. I painstakingly went through each this morning ensuring that every setting I can possibly control is identical.
I've wasted so much time on it already that I'll leave it be and just retrieve mail from the mail host's website and hope that it's one of those things that will spontaneously rectify itself. Thanks for your suggestions. I've come to accept that Outlook is regularly troublesome.