I'm guessing it's either:

a) Low battery

b) Overheating

c) Bad motherboard

To narrow the choices down: Is it on wall power? Is the fan going crazy right before it happens?

Your computer is telling you to back up Right Now. Do not ignore it.
* Then check the event log to see if there's anything useful in it.
* There's software that monitors laptop temps; google it up and do a free trial.
* Make sure the power adapter is okay - no loose connections.
* Check the battery - some laptop batteries have a status indicator that will also let you know if the battery is broken - the lights will blink.
* At startup, tap F12 to get the boot menu. Run diagnostics.
* Fn + Esc is the Suspend shortcut. Could you be hitting it accidentally?

CMonkey is probably right,

But, it could also be the graphics card overheating / crashing.
Are you sure that the machine has gone to sleep.

To test:
Start playing some mp3s
open and close firefox a lot. Move firefox around.
When the machine "sleeps" can you still hear the music?

If so, try reducing the Graphics Acceleration.
And drop the colour depth.
Does that make a difference?

Oh, and the LCD might be dying. If you have an external monitor, try plugging that in when it happens.

An Optiplex is a desktop box.

My vote is lousy mains power. Are you using an Uninterruptable Power Supply? They can clear up many shifty gremlins.

Also: Dell shipped you a bootable diagnostics CD. Boot from that, and have it run its' default tests for a few loops. If it's bad hardware, that should catch it.

Newish Optiplexes also have diagnostic lights in the back, near the USB ports. They should all be green when the machine is running.

Also, Google "Optiplex Bad Capacitor" and see if that applies.

Thank you, all. . .this gives me a lot to go on.

I now have, thanks to seanyboy, a reason to have mp3's playing all day. Just doing diagnostics.

A couple months ago, I DID spray superglue all over my screen on my LCD monitor. Don't ask, but it has not seemed to affect the performance, and I can only see the effect from the side, not front on.

'nother thought: I've had problems with the add-in DVI graphics cards in Optiplexes. (It's the card with the white, rectangular connector and large heatsinks)

There's also on-board VGA graphics, and Dell just puts a plastic cap over the connector. An additional graphics card disables the on-board, so (if you have one) pull the DVI card and try the onboard graphics (blue, trapezoidal connector, 3 rows of pins).

We had that bad capacitor issue at work with the Optiplex GX270 series. I've replaced about 25 motherboards so far. If you open up your computer and look at the motherboard you can see the capacitors around the processor are covered in crud or maybe have an orange tinge. Definitely worth a quick look just to rule that out.

Talkie Computing