It seems that there was a nagios account created, but no home directory created for it, even the home dir path was shown in /etc/passwd. So I followed all your commands.
nagios
snmptt
amavis
postgres
ajaxterm
[root@itmon /]# cd home
[root@itmon home]# ls
irog snmptt
[root@itmon home]# mkdir nagios
[root@itmon home]# chown nagios:nagios ./nagios
[root@itmon home]# ls -la
total 20
drwxr-xr-x. 5 root root 4096 Dec 12 12:04 .
dr-xr-xr-x. 27 root root 4096 Dec 10 16:11 ..
drwx------. 4 irog irog 4096 Jan 29 2013 irog
drwxr-xr-x 2 nagios nagios 4096 Dec 12 12:04 nagios
drwx------. 3 snmptt snmptt 4096 Jan 4 2013 snmptt
[root@itmon home]# grep nagios /etc/passwd
nagios
[root@itmon home]# cd ..
[root@itmon /]# service crond restart
Stopping crond: [ OK ]
Starting crond: [ OK ]
[root@itmon /]# tail -25 /var/log/cron
Dec 12 12:04:01 itmon CROND[9517]: (CRON) ERROR chdir failed (/home/nagios): No such file or directory
Dec 12 12:04:01 itmon CROND[9516]: (CRON) ERROR chdir failed (/home/nagios): No such file or directory
Dec 12 12:04:01 itmon CROND[9518]: (CRON) ERROR chdir failed (/home/nagios): No such file or directory
Dec 12 12:05:01 itmon CROND[9579]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/eventman.php > /usr/local/nagiosxi/var/eventman.log 2>&1)
Dec 12 12:05:01 itmon CROND[9577]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/perfdataproc.php > /usr/local/nagiosxi/var/perfdataproc.log 2>&1)
Dec 12 12:05:01 itmon CROND[9580]: (root) CMD (LANG=C LC_ALL=C /usr/bin/mrtg /etc/mrtg/mrtg.cfg --lock-file /var/lock/mrtg/mrtg_l --confcache-file /var/lib/mrtg/mrtg.ok)
Dec 12 12:05:01 itmon CROND[9582]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/nom.php > /usr/local/nagiosxi/var/nom.log 2>&1)
Dec 12 12:05:01 itmon CROND[9581]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/reportengine.php > /usr/local/nagiosxi/var/reportengine.log 2>&1)
Dec 12 12:05:01 itmon CROND[9583]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/sysstat.php > /usr/local/nagiosxi/var/sysstat.log 2>&1)
Dec 12 12:05:01 itmon CROND[9585]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/feedproc.php > /usr/local/nagiosxi/var/feedproc.log 2>&1)
Dec 12 12:05:01 itmon CROND[9584]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/dbmaint.php > /usr/local/nagiosxi/var/dbmaint.log 2>&1)
Dec 12 12:05:01 itmon CROND[9586]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/cmdsubsys.php > /usr/local/nagiosxi/var/cmdsubsys.log 2>&1)
Dec 12 12:05:01 itmon CROND[9587]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/cleaner.php > /usr/local/nagiosxi/var/cleaner.log 2>&1)
Dec 12 12:05:01 itmon CROND[9591]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/deadpool.php > /usr/local/nagiosxi/var/deadpool.log 2>&1)
Dec 12 12:05:51 itmon crond[10079]: (CRON) STARTUP (1.4.4)
Dec 12 12:05:51 itmon crond[10079]: (CRON) INFO (running with inotify support)
Dec 12 12:05:51 itmon crond[10079]: (CRON) INFO (@reboot jobs will be run at computer's startup.)
Dec 12 12:06:01 itmon CROND[10106]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/sysstat.php > /usr/local/nagiosxi/var/sysstat.log 2>&1)
Dec 12 12:06:01 itmon CROND[10107]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/cleaner.php > /usr/local/nagiosxi/var/cleaner.log 2>&1)
Dec 12 12:06:01 itmon CROND[10108]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/eventman.php > /usr/local/nagiosxi/var/eventman.log 2>&1)
Dec 12 12:06:01 itmon CROND[10109]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/cmdsubsys.php > /usr/local/nagiosxi/var/cmdsubsys.log 2>&1)
Dec 12 12:06:01 itmon CROND[10110]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/perfdataproc.php > /usr/local/nagiosxi/var/perfdataproc.log 2>&1)
Dec 12 12:06:01 itmon CROND[10112]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/feedproc.php > /usr/local/nagiosxi/var/feedproc.log 2>&1)
Dec 12 12:06:01 itmon CROND[10115]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/reportengine.php > /usr/local/nagiosxi/var/reportengine.log 2>&1)
Dec 12 12:06:01 itmon CROND[10114]: (nagios) CMD (/usr/bin/php -q /usr/local/nagiosxi/cron/nom.php > /usr/local/nagiosxi/var/nom.log 2>&1)
[root@itmon /]#