Gradual frame drops all the way down to the 10s.

[Rekh]

That sounds like overheating to me.

What are your cpu/GPU temps when the framerate starts dropping.

Yes, it also sounds like this might be the issue.
To add to this, it could also be a dieing power supply. Not getting enough power can also do this. What's the wattage for your power supply?

For now I'd monitor both temperatures and cpu/gpu/hard drive usage in task manager.