I'm using the litespeed 4.0.13 enterprice version. i got the same issue the auto-restart on server configuration doesnt seem to work. the site was went down 2-3 times per day, i have to ssh manually restart the litespeed.
my case is different, there are 2 lshttpd was running with 100% CPU usage, my linux box still have ard 1GB ++ free memory available when the litespeed went down.
btw i have enable both Auto Restart and Auto Fix 503 Error.