And then I found that the clock drift was really bad, and NTP wasn't working for some reason.
http://kbase.redhat.com/faq/FAQ_43_9259.shtm suggested adding the following line to the .vmx file:
tools.syncTime = "TRUE"
This (by itself, anyway) didn't work for me.
http://www.djax.co.uk/kb/linux/vmware_clock_drift.html suggested appending the following items to the kernel command line (in lilo.conf or grub.conf):
nosmp noapic nolapic
That worked like a charm. That article also suggested appending '
clock=pit' if the guest clock runs fast (mine was running slow).