Ah. Last Friday at work I changed my password. It worked fine when I unlocked my computer after stepping away. On the way home, I noticed that my iPhone wasn't updating email, and recalled that I hadn't changed the password there. But I could not get the iPhone to accept my password. Nor could I get Outlook webmail to accept it. I was afraid that I might have to trouble one of the network admins, but I tried the VPN client. That accepted the password. I RDPed into a machine on the internal network, changed the password to something a little shorter, and confirmed that Exchange was OK with it.
As I recall, the boundary was somewhere around 20 characters.