Intel Skylake HDMI No sound at all after monitor wake

[Nick Breen]

Reproduction:
1. Boot
2. Select HDMI from Sound Settings
3. [sounds play]
4. Monitor sleeps (PC does not)
5. Monitor wakes
6. No sound, HDMI is missing from Sound Settings
7. Re-plugging the HDMI cable restores the option, repeat from 2.

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: alsa-base 1.0.25+dfsg-0ubuntu5
ProcVersionSignature: Ubuntu 4.4.0-66.87-generic 4.4.44
Uname: Linux 4.4.0-66-generic x86_64
ApportVersion: 2.20.1-0ubuntu2.5
Architecture: amd64
AudioDevicesInUse:
 USER PID ACCESS COMMAND
 /dev/snd/controlC0: nick 2851 F.... pulseaudio
 /dev/snd/controlC1: nick 2851 F.... pulseaudio
CurrentDesktop: Unity
Date: Mon Mar 27 13:26:19 2017
InstallationDate: Installed on 2016-10-28 (149 days ago)
InstallationMedia: Ubuntu 16.04 LTS "Xenial Xerus" - Release amd64 (20160420.1)
PackageArchitecture: all
SourcePackage: alsa-driver
Symptom: audio
Symptom_AlsaPlaybackTest: ALSA playback test through plughw:PCH failed
Symptom_Card: Built-in Audio - HDA Intel PCH
Symptom_Jack: Digital Out, HDMI
Symptom_Type: No sound at all
Title: [, Intel Skylake HDMI, Digital Out, HDMI] No sound at all
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 08/17/2016
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: KYSKLi70.86A.0041.2016.0817.1130
dmi.board.name: NUC6i7KYB
dmi.board.vendor: Intel Corporation
dmi.board.version: H90766-405
dmi.chassis.type: 3
dmi.chassis.vendor: Intel Corporation
dmi.chassis.version: 1.0
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvrKYSKLi70.86A.0041.2016.0817.1130:bd08/17/2016:svn:pn:pvr:rvnIntelCorporation:rnNUC6i7KYB:rvrH90766-405:cvnIntelCorporation:ct3:cvr1.0: