I am sort of new to the linux (RHEL4) environment, so I am not really sure where I should go from here. On tru64, I can attach to a process, slapd in this case, I am not sure how to do that in linux.
At least in the case where slapd is unexpectedly exiting, you can install gdb on your system. Find the pid of slapd on your system, then run gdb, then "attach <PID>" at the gdb prompt. gdb will then tell you if slapd is catching a signal (which seems to be your working hypothesis). There are some basic instructions on generating a usable stack trace in the OpenLDAP FAQ-O-Matic.
If gdb reports that you are indeed seg faulting, it might be worth installing valgrind and seeing if that produces anything enlightening. Feel free to discuss your progress here, but you should formally report any issues you find via the ITS.