OK, I have an emachine monitor (and PC). I admit it was a Wal-Mart special because we were in a pinch. Anyway, without warning, without rhyme or reason…the monitor will just blink out (turn off for a brief period). My wife says sometimes it’ll do it four times in a row! Should we be worried it’s going to die?
Is this the price I must now pay for cheap electronics? - Jinx 
It’s either the monitor or the video card. You can get a cheap video card (graphics card) for under $50. You can get a refurbished monitor for about the same. In my expericence, it is more likely the video card than the monitor, but if you hear a snap sound like an electrical arc when the monitor goes out, then I would say it is more likely the monitor that is at fault.
A cow-orker recently had this problem. I took a look before we called the IT people, since they’re notoriously unresponsive.
The back of her monitor was pressed all the way against her office wall, and the pressure point was right on the power cable. If she put any additional pressure on her desk at all, like leaning on it, opening drawers, etc., the cable would come out of the back of the monitor just enough to turn it off. She’d stop doing whatever it was she’d done, and it would come right back on.
An easy fix. Hope yours is, too!
Maisy
Perhaps a silly thing but check to see you do not have power saving settings turned on and set to some very low time (like 1 minute before the monitor turns off if the PC does not see any action from the user).
Check your power cable connection. This used to happen to me with my monitor and the connection was loose. I just had to push it in a bit more and it was OK.