I had a similar issue a couple of years back. All was okay, the very first time I played Crysis. No crashes or BSODs from start to finish, and this was on XP32.
I later upgraded to XP64, and decided to play through Crysis again, via the 64bit version. Again, all was decent from start to finish. In fact, I'd go as far as saying that I found the 64bit version smoother.
It was after I'd left the game for 6 months, then decided to play-through again, that I experienced BSODs. They'd happen fairly randomly, and the performance had taken a hit as well.
It really suffered in the battles after defeating that 'hunter' alien (big spider thing). I couldn't figure out why at first, especially since it was the same installation, which worked all those months ago.
I tried re-installing; checked all my drivers and directx version, but the BSOD issues persisted. I then decided to test my RAM using Memtest. Basically, a diagnostic app, loaded outside the Windows environment, to test memory modules for faults. Sure enough, I found faults in 2 of my RAM sticks. I returned them and received replacements, and BSODs vanished.
My advice, try running Memtest to check your memory modules for faults !! If you're not too familiar with it, the website is here...
Memtest - Downloads
I'm not saying this will solve your problems, but it's a useful tool to have, and couldn't hurt to try