I've discovered that if 'Auto Logout' (Administration, System, Basic Config) is set to a large value (960 minutes), the web UI stays logged in, as intended, and httpd does not crash. Setting the Auto Logout to zero (0) will cause httpd to crash after some random amount of time. Try setting Auto Logout to a large number.
I had the automatic shutdown set for 20 minutes. Thanks, I'll try it.