I believe I have solved why Steam Recordings don't record audio sometimes.

[MyOneAndOnly AndYoursTruely]

I've listed potential troubleshooting issues and noted what has fixed the no audio recording from Steam's Recordings and Screenshots feature.

[MyOneAndOnly AndYoursTruely]

SO this is the Problem Discussion:

I believe there are two main ways that Steam Recording fails to record Game Audio. The First is in your PC Settings. It is likely an Audio Device labeled "Steam Streaming Speakers" that was somehow silenced.

Second possible problem is that the game needs to hear EXACTLY what you hear. This includes all the sub-settings in your audio.

Additionally, out of reach, there may be updates that your computer needs.

[MyOneAndOnly AndYoursTruely]

As for the Solutions Discussions: [Windows]

This is what you need to checklist off:

1. Please check your Volume Mixer Settings and Reset sound devices and volumes for all apps to the recommended defaults. You can do this by going to your PC Settings > Sound > (Scroll Down) Volume Mixer > Press Reset
   
   
2. Ensure that you have NOT enhanced your audio in anyway. Go to your Sound Settings > [Select the audio device properties that you are currently using] > In the Advanced settings category, turn everything OFF
   
   
3. Are all your drivers up to date? Go into your graphics card driver hub and/or your OS and see if it requires a system update.

[MyOneAndOnly AndYoursTruely]

As for Optional Solutions:

If the above don't work, you can make do with these alternatives:

1. Change your Recording Settings to ALL System Sounds. This can be found in Steam Application by going to Steam > Settings > Game Recording > Record Audio from... > Select: All System Audio.
   
   Do be aware by doing so, it will capture ALL of your computer audio, including reviewing footage of recently captured clips, potentially leading to feedback loops of the same audio.
   
   
2. Use a Third Party application to align your Main Audio Device with the same as the Steam Streaming Speakers. You can use a free software like VoiceMeeter, set VoiceMeeter as the Default Audio Output, and in the VoiceMeeter application set your A1 Output to Steam Streaming Speakers and A2 to your preferred speakers.
   
   Do be aware by doing so, this will lead to marginal latency or visual to audio desync by a few frames. This is NOT recommended in competitive settings, however if you are recording audio, you can always video edit the audio to be a few frames forward to sync with your video