If the house power shuts off when my mac is in SLEEP MODE!

Always that your Mac is turned on (when it's in sleep mode, it's turned on), there may be a risk to get hardware damaged if power goes off. However, the hard disk isn't in use when your Mac is in sleep mode, so you shouldn't have any problem with it, but that may happen. In your case, the problem will be OS X, that will shut down unexpectedly without closing apps. That's the main problem, because OS X may get damaged, so you will have to reinstall the operating system.

To be safer, I recommend you to turn off the computer instead of putting it into sleep mode until your house power is better, but if you want, use sleep mode at your own risk

I too have a Mac Mini and an UPS. However, with Mt Lion I can not put the Mac to sleep mode. I know that there is a Terminal "fix" for it. But with this Mac using so little power, there is no difference if the Mac is "awake" or "asleep". So I just leave it on all the time, I just used the lower left hot corner to turn off the display.

With that being said. I have my UPS attached to my Mac Mini via an USB cable. The Mac recongize it and gives me options on how I want the Mac to react when the UPS is on battery.

Under System Prefernces then Energy Saver. You'll see two tabs, the default one is Power and the second is UPS. Click on UPS and you'll be given two scroll bars. The top one is "Computer sleep:" in whatever time you want it. But again for Mt Lion it won't go to sleep. So I have this on Never. The bottom one is Display Sleep, I have that set to 3 minutes. As for the three check boxes, Allow power button to put... Slightly dim the display when... and Automatically reduce brightness before... are all unchecked.

Where you want to go is to Shutdown Options. That will bring down another menu. There will be three scroll bars. The top is Shut down the computer after using UPS battery for X amount of time. Then Shut down... when X amount of time is remaining on the UPS battery. Lastely Shut down the computer when X amount of battery level is left.

Personally I have mine set on the last at 3% battery level. So when the battery reaches 3% battery level, the Mac Mini will do a proper shut down by itself. I do not have to be present when this is done. As a matter of fact, it has done it when I was away at work.

Before I posted this, I did a little test. I opened MS Word 2011 and started to type. Turned the display off and unplugged the UPS from the wall. After a minute, because I temporally changed the settings, the Mac shut down. But even though every window and app that I had opened before the shut, opened back up after I turned the Mac back on. MS Word did not save the work. So basically, save your work when you leave. lol.

If your UPS doesn't support a USB cable connection. I suggest getting one, they are rather cheap now a days, and put your current on your modem/router area. So that you can continue to go on line when the power goes out. I have done it a few times and lastest about an hour til the UPS finally shut down from a drained battery.

One more then, when your UPS goes on battery. A little warning comes up on your display. "Warning! your computer is now running on UPS backup battery power. Save your documents and shut down soon." You can click the "ok" button. But if you are not home and you go by what I said above, the computer will still shut down properly.

Enjoy,

KOT

I would uncheck "Start up automatically after a power failure" in the Energy Saver Preference, that way the Mac Mini will not cycle off/on/off/on when your not around.