Hi Abhishek, if you have tried the things below, please disregard. As a general rule, when DevTest stops one of its services, DevTest produces some type of message in the log. Since you are apparently not seeing any DevTest generated messages, it leads me to wonder if something external to DevTest is stopping the service.
If it is possible in your environment, stop all of the services, access lisatmp_dir and either remove or rename the current set of registry, vse, vse_matches, etc. log files. Edit LISA_HOME logging.properties and set the logger to DEBUG. Restart each of the services. When VSE crashes, research both the vse and registry log to see if you see any exceptions, warnings, unusual display messages, etc.
You might look for an INFO or warning message that looks fishy, or some other display message that might indicate why the service is stopping.
If this is a Windows server, try looking in the server's Event Viewer and see if an error or warning shows up there for the VSE process. If Linux, try to see if something in the kernel.log can help you.