After a recent update to cPanel/WHM 9.9.9, outgoing emails stopped working on the RHE server (CentOS server wasn't affected).
Found this fix:
/scripts/exim4
/scripts/upcp
if that doesn't work... do
/scripts/scripts/reseteximtodefaults
also... you may want to try this route:
/scripts/exim4 -latest
/scripts/buildeximconf
/scripts/updatenow
/scripts/restartsrv_exim
TEST FOR RELAY:
http://www.abuse.net/relay.html