TLDR: Set the HDMI output resolution on your PVR to 1080i instead of 1080p, and the component outputs on your FibreOp PVR will start working again, and therefore your Slingbox will start working again.
I purchased a Slingbox 350 a few years ago for the rare time I want to watch something on TV when I'm on the road. For the most part, it's worked well--although the very tiny bit of TV I watch hasn't really justified the cost.
Recently, however, it stopped working, for no apparent reason. After a few hours of searching for similar problems and monkeying around with the firewall on our ActionTec router (which, BTW, has not had a firmware update since it was installed two and a half years ago: how about that mess of security vulnerabilities) to open up a port that was never required before, based on advice from about 4 years ago, I was no further ahead.
Then I remembered that our PVR received an update just before Christmas that introduced a brand new UI and features like Santa Tracker. "Hmm", thought I, "could this be related to the problem?" I dug into posts about the update and discovered someone in the middle of a thread about a different feature complaining about their component output ports no longer working after the update, which lead to this thread pointing out that only the video on demand content was available in 1080p anyway. (Warning: those forums have obnoxious autoplay video ads!)
"But wait", I thought to myself, "I've never changed that setting, why would it be set to 1080p now?" As far as I can tell, it was purely a result of the update. Changing the output resolution setting back to 1080i enabled the component outputs to start pumping out data again and gave the Slingbox something to sling.
I wouldn't mind getting those troubleshooting hours of my life--more than I spend most weeks actually watching TV--back, even though figuring out the solution did eventually provide some satisfaction. For the most part, I have only myself to blame: I've put myself in a situation where I'm relying on a ton of proprietary software and hardware (Slingbox, ActionTec router, Arris PVR) over which I have very little control, and no ability to dig into the internals to see what has changed. Hopefully this helps someone jump directly to the solution.