When I delete /var/log/secure this file will be recreated. How do I disable the recreation of this file?
/var/log/secure is written to by syslogd (or rsyslogd, depending on the OS version) -- this is controlled by /etc/syslog.conf (or /etc/rsyslog.conf). As shipped, the log class "authpriv.*" is set to log to this file. If you don't wan't logging, your can comment out this selector from the .conf file.
Also, check the logrotate configuration (/etc/logrotate.conf, /etc/logrotated.d/) for the rotation script for syslog. This will typically re-create the file (although the file won't be growing if you comment it out of /etc/rsyslog.conf).
If you cannot find the program that writes that file, and disable that program or if you cannot prevent it from being run, you can try and create the file and change the permission:
Depending on how the program that writes to the file works, this might prevent it from updating the file. But it could also cause the program that writes the file to complain or even to crash.
*Of course you end up with the file being there, it would not be recreated and/or updated. But if the creating program removes/renames the old /var/log/secure before it starts writing the new version there is little you can do without changing the program or its configuration.