Exim is mysteriously crashing, usually when forking to send a delivery error message.

This has been seen in cases where Exim has been incorrectly built with a muddled combination of an ndbm.h include file and a non-matching DBM library. Faults like this have also been seen on systems with faulty motherboards. You could try to compile the Linux kernel 10 times - if the compile process stops with signal 11, your hardware is to blame.