MySQL crashes daily on VPS with Ubuntu Server 12.04 - How can I find the error or conflict?
Check the value of the variable "log_error":

select @@log_error


or

show variables like 'log_error'


It defaults to /var/log/mysqld.log on a RHEL6 server though can be different.

Then check this log file - it will generally give you a reason why it's failing.  

Alternatively, if the service is being killed because the server is running out of memory, check the system log:

/var/log/messages 


For the "Out Of Memory killer" doing it's thing or any other messages that might be relevant around the time that the server died.