Are you using a soundbar?
Have you tried changing Match frame rate on the 360 via Settings > Audio & Video > Match frame rate? If it's set to ON then people do see a blackout/or hear a sound drop when the 360 or HDMI reconfigures for the difference in frame rate.(This is more noticable on live TV when switching from adverts back to a program, or changing channels)
If it's set to the default (OFF) then the box just accepts the frame rate difference which isn't noticeable by most users and shouldn't blank the screen out. (Either way try toggling this setting to see if it improves your issues)
Also what is selected under Settings > Audio & Video > Audio output ? There are 3 options > Follow Content, PCM 5.1 (HDMI only), and PCM 2.0
Choose whether you want the audio output to follow the quality of the original content (Dolby Digital where available) or to be converted to PCM 2.0 (stereo) or PCM 5.1 (uncompressed multi channel sound). Using PCM settings may resolve audio sync issues. Netflix will always use Follow Content. Use 'Follow Content' for any bitstream audio like Atmos where it's available on content.
Duplicate post with https://community.virginmedia.com/discussions/Virgin_TV_360/360-box---audio-sometimes-drops-out-from-sound-bar-hdmi-arc/5612799