Starting fast then slowing down sounds like a thermal issue. Check your temperatures before starting the game, then after it gets slow.
Perhaps try running with the case open and a large fan blowing into the PC - if it runs longer before slowing down, then you may be able to ameliorate the problem by improving the cooling in your PC. Could be graphics card cooling, could be CPU cooling - I'd suspect the graphics cooling, as a first guess. You could change the cooler on the card, or add/replace fans in the case - more air blowing through the case might be all you need (it's an easier fix than replacing the cooler on the card). Case fans can improve CPU cooling, too.