Can't help with core files, but would suggest you reduce the problem to the
smallest set of "things" that trigger it.
Try different machine, different RAM, different NICs. If you've got a similar
machine, move the HD into that machine and see if you get the same behaviour.
Try starting with base install, and slowly moving up to the level you need -
perhaps on the way up you will find the trigger.
AND/OR ...
[You might already be achieving this with symon, etc.]
Write a script that logs to a file (might need to flush after the write) every
5 minutes or whatever; maybe write the output of ps (or whatever interests
you) to the file.
See what time(s) the crash happens and drill-in on that time with more
diagnostics. If the crash is always happening at 8.05 p.m., you can start to
investigate more what happens at that time of day.