The admin-console provides the operations "Start", "Restart", and "Shutdown" for the EAP server. If you browse to the admin-console, authenticate, and then select "JBoss EAP 5 (default)" under the "JBossAS Servers" in the left hand pane, you can invoke the Restart operation. EAP will shutdown (the JVM exits) without a subsequent start up (The page loads with errors as well).

This is due to the run.sh/bat script being broken. The original AS start scripts had logic that would check the exit code form the AS JVM and perform a restart in certain conditions, however, it appears that sometime in EAP 4.3 this functionality was broken.