rsync over remote ssh Error 7077010011

A backup job using rsyn over remote ssh has just failed.  It's been working for quite some time, but now without warning, kaput!

When I try to test the connection, I get the not-terribly-helpful-or-meaningful error 7077010011.  The logs give a little more insight:

Backup Status: Fail: Failure during copy.

Failed to run rsync, return rc 255
Permission denied (publickey,password,keyboard-interactive).
Permission denied (publickey,password,keyboard-interactive).
rsync: connection unexpectedly closed (0 bytes received so far) [Receiver]
rsync error: unexplained error (code 255) at io.c(235) [Receiver=3.1.3]

Uhm, okay... looks like some problem with the key.  The key has been imported to the destination, is one of the members of the 'authorized_keys' file.  But again, this has been working, and to my knowledge nothing has changed.  The NAS is still connected using the same IP address, the destination IP is the same, and nothing in sharing settings, file system, etc has changed.  I've even checked the content of root, admin, and my user id_rsa.pub keys, and they all agree with those stored on the destination.  Arrrg!

What could have have happened, and how can I better go about troublshooting this?