Gigabyte Z370 Gaming 7 looks like it has an issue with the sound card intermittently dropping out causing the driver to reload which would explain how you are exposing FFXIV's audio bug. Looks like some people solved the problem by turning off Crystal Voice but others had to completely disable it and use another sound card.
Shut your computer off completely and let it sit for about a minute and then turn it back on. I bet that will prolong how long it takes for audio to stop working which leads me to believe its a hardware issue with the motherboard.
edit: you should be able to see if this is the case by disabling the onboard sound system in the bios and using HDMI audio output on your video card. If the problem goes away you isolated your problem.
edit2: The above looks like its for the Z270 not yours. Seems like gigabyte has a lot of audio issues lately. You can try downloading different drivers and see if that fixes your problem:
https://www.tenforums.com/drivers-ha...r-version.html