I tried increasing kern.maxfiles:

	# sysctl -w kern.maxfiles=1048576
	kern.maxfiles: 1772 -> 1048576

	Which does not help.  The system does not have very much going on, certainly
	nothing that would keep a large amount of files open at once.  Has anyone
	else seen this problem?

Once you've increased kern.maxfiles you then need to increase
your ulimit for descriptors.

Eduardo