UPS killing my A3000UX?

[AMC258]

Once in a while, after leaving my Amiga unattended for 12 hours or so, I get to it and it is crashed.  No video, and no warm resetting!  Nothing.
I have not been able to figure this out until just now, maybe..

I have my A3000UX plugged into several UPSs.  All APC's, all different.  They all do what they're supposed to.  The one the motherboard power supply is plugged into just made a weird blee-EEeeep and cut the power to my Amiga for I'd say about 50ms!  And, the A3000 went into the state stated above.
Obviously, this is really really bad.
Has anyone else had such a problem with a UPS?

[AMC258]

I can already do that with my Amiga.  I don't have a robotic video camera though, but I certainly do have the ability to have one.

The UPS on my A3000UX's motherboard is an old APC (the very reliable ones) with relatively new batteries.  It is not running near full capacity, and I have tested it in this state.  In that case, it will give a coded beep pattern and eventually turn off, only to turn back on if you clear the fault and turn it on manually.  The batteries also check good.
I have maybe 2 dozen UPSs on computer equipment throughout my house.  I even had one on my furnace for a while.  I have never actually had any problems before.

Oh, and my power goes out all the time.  My power company is Weenergies, (yes that's really their name), and they are "Voted Best in the Nation for Keeping the Power On!"  The key word there is "voted".  I sure didn't get a vote!  I often wonder who it was that did vote!

[AMC258]

Their logo is the same as the Women's Entertainment logo too..

I have actually lost many things due to power problems in the past.  C64 and 1526 printer included!