As an update to this thread, I recently downloaded Opera_57.0.3098.110_Setup_x64.exe just to see if the update function worked properly on an earlier version. It did.
I don't know which version hosed the update functionality but there is something different since at least Opera 57 because Opera 57 automatically updated me to the latest version...
And, of course, the latest version no longer does automatic updates and shows the greyed-out "Check for update" button.
Sigh...