as suggested by Chirpy and got the following error:
DBI connect('eximstats:localhost','eximstats',...) failed: Client does not support authentication protocol requested by server; consider upgrading MySQL client at /usr/local/cpanel/bin/eximstats line 264
Can't Connect at /usr/local/cpanel/bin/eximstats line 267.
This command did seem to fix it (at least I am not getting the error email anymore).
I also checked the /etc/my.cnf and found that it did not say "old_passwords" even though I did check mark this in WHM. I went ahead and added it and restarted, even though I wasn't getting the error anymore about eximstats.