I don't know what caused the original problem, but here's some information about getting the webAccess restarted after a failure. I was able to get things restarted without rebooting any virtual machines or the host machine. In my case, there was a broken version of the Tomcat web application server still running. I had to kill that and restart the vmware-mgmt service. Things started working again.
Specifically...
1) Try to stop the service through the service interface
service vmware-mgmt stop
2) Ensure that it terminated properly
ps -elf | grep catalina
3) If you see any Tomcat processes (they end in 'org.apache.catalina.startup.Bootstrap start', kill them using the 'kill -9 <pid>' where the <pid> is the 4th field in the ps -elf command. For us Unix geeks, the command is
ps -elf | grep catalina | grep -v grep | awk '{print $4}' | xargs kill -9
4) Restart the service via the service interface
service vmware-mgmt restart
Of course, that's not a solution, but it may help some of you get operational again without any reboots.