It could be temperature related. Many companies, trying to be more energy efficient, shut down the Air Conditioning at night. I would run Console and check your log files. You should be able to see if a chron job or temperature is shutting it down.
If you do not understand what Console is, someone will either need to do some studying or hire a Unix Guru. You may be able to send the logs to Apple Support, if you have a Service Agreement. It is far beyond the scope of this site to instruct how to analyze log files.
If you think it might be temperature related, leave the door to the room the server is in open (put furniture in the way with a 'do not move' sign) or put a cheap box fan (less than $20) where it will blow air on the server and see if it stays up that night. Note: this is a test, not a permanent solution.
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