I just diagnosed this problem on my VSX882k. It was a bad mute relay on the output of the INPUT board, NOT the mute relay on the AMP board speaker outputs. The input board basically supplies the line level outs to the power amp section. Same issue, center channel drops in output, sounds distorted. Sometimes if you crank the volume, it will work again, but only temporarily. Powering it down and back on occasionally works too. It opens and closes the relay, and sometimes it closes properly. The relay part number for the VSX822k is HL3-2A-12S. I would not be surprised if that's a common relay part # across the VSX series of AVR's. The only place I could find it in the US was on eBay, and it's coming from China. I got ten of them for $16 w/shipping. Hope this helps someone.
EDIT: On the 822k schematic, it's RLY 402