I have the exact same problem as MacScottie.
Every time, I play A3 (Wasteland, sa-matra-version), my fps drop after a while (around 20-50 minutes, I'd say) to 3-7 from 30-40. Just out of nowhere the game becomes unplayable.
Flush does nothing. Only a restart helps.
I would like to keep playing Arma3, but like this, there's no point. Finding decent gear in Wasteland, or going on missions is completely useless if you constantly have to reconnect.
The game does not recover from itself, unfortunately.
i5-3470 @ 3.20GHz
120GB SSD
8GB Ram
Windows 7 64bit
ATI Radeon 7850