When playing Mirrors Edge the framerate drops until it is unplayable and runs at 1-2 FPS. At all other times it's fine, and opening to the main menu and resuming resolves the issue, as does quitting and then returning back to the game. The most recent time is when I've got to Ropeburns Office and I'm climbing up the waterfalls, I jump across to the balconies and when I get shot at the frames drop to next to nothing.
I'm running on a quad-core AMD 2.8Ghz with 8GB of RAM from a OCZ SSD and a ATI Radeon 7870 Core graphics card. I didn't have any issues when playing on my laptop - Dual core 2.0Ghz Intel with 4GB RAM and integrated graphics.