CentOS 5. The problem is that you probably hit your process limit when doing it via cron, so it fails. Nothing you can do about that unfortunately. Make a script that runs the first command, then renames it perhaps? Users do not have SSH, so no way to really test why its failing. That command has nothing wrong with it (I omitted the -P, you may or may not need that -P argument) when I run it though.
rax@rax.heliohost.org [~]# mysqldump -u rax rax_si3sys > backupfile`date +%y%m%d`.sql
rax@rax.heliohost.org [~]# ls
access-logs@ cpbackup-exclude.conf mail/ public_ftp/ skmaildb/ ssl/ www@
backupfile160421.sql etc/ perl5/ public_html/ softaculous_backups/ tmp/
rax@rax.heliohost.org [~]#
The backupfile160421.sql is a proper dump of the database.