I changed a number of components in my system - most notably the processor - and while I haven't had any drops lately, I'm on a processor that seems to get HDMI a bit... "wrong." The sound quality is simply fantastic, but there seems to be a problem when HDMI changes mode, and audio isn't muted long enough while that happens so there is a single click or pop that occurs.
While the click is far worse on the AppleTV than other devices, I can't say it's the sole fault of Apple. Other owners of devices in the same processor family have been eagerly waiting for months for a firmware update that fixes it. If that is released soon, I can report back if it improves or resolves the AppleTV issue. I tend to run the volume at a much higher setting on AppleTV than my DirecTV feed - Apple seems to have a different philosophy behind their native gain levels - so that probably is the reason for the "pop" being much more noticeable on AppleTV.
I have an in-wall HDMI cable that I plan to replace too, to see if that helps. Belkin doesn't make one quite long enough, so I ordered a Wireworld cable that supports 48Gb bandwidth and 8k video, meaning I should be future-proof for 5+ years. I'll definitely post if that has any positive impact.
