Down near the bottom, search for "core dump" I think.
So is the desktop crashing or just locking up? If locking up, what does that mean, can't control the mouse, or other stuff? Sometimes the VM software (VirtualBox, VMWare, etc) can "capture" the mouse if it's running windowed and it can seem like things locked up.
When it went bad, doing top showed nothing spinning at 100% cpu? ps -ef shows nothing weird (like no desktop processes)? Is gdb installed on the host? If it is and something looks like it's taking up lots of CPU, use gdb to attach to the running process and type in "bt" (back trace) to get a quick stack dump. That tells you where something is.
I ran into a weird one at work, a laptop with Intel i915, running RHEL. Things would appear normal until you did "xset -dpms" then the Xorg process went to 100%. SSH into the machine would be fine, killing X would bring it back to life. Turned out to be a "nomodeset" on the grub boot line (cat /proc/cmdline to see how your kernel booted). i915 graphics needs kernel mode set support enabled.