I'm having porblems playing assassin's creed 2 for I've been experiencing stuttering problems constantly (completely maxed out but changing settings doesn't solve the problem) and recently I installed batman arkham asylum which ran perfectly but after about 2 hours or a bit less, it begins to have a ton of lag and it becomes practically unplayable.
These are my system specs: intel core i5 2400 3.1 ghz
asus radeon hd 6850 v2(it has 2 6-pin power connectors)
8gb ram 1600mhz (g.skill sniper)
hdd 500gb wd caviar blue
spu sentey solid power 550w (sdp550-ss would be the model)
I play both games maxed out at 1366x768. I'm also playing skyrim in the same conditions and experience no lag whatsoever.
I'd like you to check the temperatures when the game starts lagging. You're looking for CPU, GPU, HDD and RAM. (CPU, GPU and HDD has sensors, so you typically can get a program like hwinfo or hwmonitor to check those temperatures, RAM sensor might be available depending on motherboard, but in case it's not just get into your case and feel it with your hand, carefully)
also, check that your windows power settings is set to maximum/full power profile. and that you don't have any other power saving programs that might affect performance.