You can use the audit system to watch for specific events. The file delete is one of them. You can see more details on how to modify this to suit your needs at:
In your case edit /etc/security/audit_control file and add the flag 'fd' for file delete.
In my experience you have to reboot every time you make a change to be sure it works. I have tried to avoid the reboots by issuing command:
audit -s
But it has not been reliable.