Hard drives are randomly ejecting themselves during video rendering on macOS Monterey

I'm using a LaCie 1TB SSD and Seagate Expansion 4TB drive to work on some video editing in Adobe Premiere and After Effects on my MacBook Pro M1 Max 64 GB, macOS 12.0.1.

I'm having a recurring and serious issue whereby when rendering a video from or to a drive, the drive will often randomly eject itself and cause the render to crash. It's mostly been happening with the LaCie and with After Effects. I'm rendering large video files, up to 20GB for a single video.

I instead had to start rendering the files from the project on a drive to my desktop and that seems to have better odds, but it is still happening. The only solution I found was to move the entire project to my internal drive and render to/from that.

The LaCacie SSD is formatted as ExFAT and connected via Thunderbolt 3. The Seagate is formatted as Mac OS Journaled. Both have < 50% capacity in use.

Any thoughts or suggestions as to the root cause of this would be appreciated.