What services are the server(s) running? Obviously, after oom-killer runs there will be plenty of memory, but it only runs when the system runs out of memory.
Do you have any swap, how much?
You need to look eg in /var/log/messages, and /var/log generally to see what the system was doing just before oom-killer kicked in.
You could also get logwatch to warn you of various things eg nearly out of swap....