Monitor goes black after a few seconds

Monitor goes black after a few seconds

I have a widescrceen Samsung LCD that goes black after it's been on for 5-10 seconds. Once the screen goes black, turning the monitor off then on again brings the image back for a few seconds. I've turned the brightness down quite a bit and it's staying on now, but this doesn't seem like a desirable permanent solution. It's worked fine for about a year until now. Any ideas?