remote desktop server shuts down periodically

HI, for the past few weeks our remote desktop server has been shutting down in the evening after hours and so we switched it to another ups and it was good for a week but then just this morning it was off again.  I was thinking that since this is a fairly new server and it never shuts down during normal work hours that it must be a power issue with the outlet in the server room.  Most of the  time when a server turns off as long as it is receiving power then it should reboot correct?  In this case, it is always in the off state in the early morning after shutting off the previous nite and someone has to turn it on.  I have been looking at the system log in event viewer and have seen the shutdown messages along with the timestamp but is there any other area i should be looking at in event viewer for these shutdowns?  Also, there are 4 new servers in this server room and they are connected to older ups units.  Could this also be a factor?  And if so why is it only happening to this one particular remote desktop server.  None of the other 3 servers have ever shut down.  Was also concerened that since this is a remote desktop server, is it possible that a rogue user is deliberately invoking these shut downs?  How would i monitor that?  Thanks.