First of all, welcome to TSF.
No problem asking questions, that's what we do here - help each other with issues...
If I understand your setup correctly, you're using the Onkyo to switch HDMI feeds and then send it out to the projector. I'm not an expert in projection systems but my guess is that the Onkyo has a momentary pause in signal that your projector senses as no signal and goes into sleep mode.
I'm a firm believer in eliminating causes. Here's one thing to try; take the Onkyo out of the loop, route the HDMI directly from the PC to the projector. If it still exhibits the behavior then at least you know its not the receiver.
Then look to the cable. 50 feet is a long run. Most sources (I Googled it) talk about 15M being the max. So you're right about at it. An amplifier might do the trick.
Then I'd look to the projector. Is there a setting that tells it how strong a signal to expect. A pause delay time? Or something similar?
Then lastly the PC. There may be a pause when switching output sources in the vid cards. The good folks in Hardware can address this if you get this far.
Probably not much help. Let us know how your testing goes.
And again, welcome to TSF - the best place on the net. Feel free to browse around and jump in when you can. We don't have many PCHT contributors so your's is a fresh look at the passion that connects us.
yustr