Start with a look at your logs:
<jira home>/logs/atlassian-jira.log will usually contain a reason for a crash. It's the application log, so it will show application level faults.
If that just stops dead, then <jira install>/log/catalina.out is the next place to look (this should contain a more system level error).
If both simply stop dead at crash time, then it is something in the operating system killing it, and you'll need to dig through system logs.
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