Late 2009 iMac keeps falling asleep while streaming video

Streaming video from my iMac worked perfectly until about a month ago (didn't download any new apps - it just started sleeping and not waking up out of the blue). I always set my mac to sleep after 10 minutes. This previously was not a problem at all, and my iMac would wake up when I requested it to stream something. Now it falls asleep after 10 minutes while streaming video and it won't wake back up. I've reset the PRAM, reset SMC, selected, "wake for network access" under energy saver, selected "prevent OS from sleeping while streaming" in PS3 media server - although I've tried other DLNA software and I have the same problem. I've googled and tried every solution that I can find, but nothing helps. I was on Mavericks when the problem started, but updated to El Capitan - no help there. It still has the same problem. At this point, I strongly suspect that it's a hardware issue. My network is wired and I'm generally streaming to a WD Live media player. Tried streaming to the PS3, and PS4, still get the same problem. It's as if my Mac OS will not accept commands from third party software anymore. I replaced the hard drive about two years ago and the system status says my hard drive is fine. Not interested in the Caffeine app. I want a solution - not a work around. Sure, it doesn't go to sleep if I set it to never sleep or sleep after 3 hours will at least let me watch most movies continuously, but I'd rather save energy when I'm not using it, and I don't want to change the energy saver settings every time I stream something.