I used to get emails about SL7 auto-updates, but the last one is dated 
11 Nov 2016.  There have been many auto-updates since then.

/etc/yum/yum-cron.conf hasn't changed, and points to the address from 
which I'm sending this.  I had tried to use another address earlier but 
that never worked.

The last update reported by email was google-chrome-stable.  The next 
one listed in /var/log/yum-log-20170101 is cpuid

The first line of output on starting yumex is:
'Can't detect the network connection state', but it then works as normal.

?

John P