We have been occasionally getting a mysterious crash with no output or logs.

Most recently, I did see this:

Errno = 12: Cannot allocate memory Mercury runtime: Could not allocate 16 bytes, exiting.

Which Prince version are you running, and on which operating system? Was any software upgraded recently? Can you reproduce the crash from the command-line? If so, please try running the /usr/lib/prince/bin/princedebug script and email me (mikeday@yeslogic.com) the /tmp/prince.debug and /tmp/prince.strace files that it generates.