There are some things you can try, but there's no general soln, although I believe some of the Big Iron systems do provide a crash-dump, but I'm not sure Linux can do that.
Basically, look for patterns eg same times every day, same progs working eg /var/log/messages will log until it crashes, so what was it doing just before it died?
Write your own daemon to check/log stuff every 5 mins eg output from 'top' for example.
If /var/log/messages can show you roughly when it crashed, checkk all the log files recs you can find for the preceding eg 5 mins ie everything under /var/log.
Try to turn off everything you don't need.