During the time I had left the computer running continuously, I was also periodically testing things that crashed the game or caused it to hang cleaning up a level, etc, requiring an Alt-F4 to get out of. To narrow down or try to find a workaround for each issue, I could crash/hang the game half a dozen times in a row...
You could actually try the game without Steam or Fraps running, but I don't think they would be enough to cause this issue. You can start the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file (by not starting it through Steam, you just will not have access to the Steamworks functions: Steam lobby and invite functions, achievement and playtime tracking). If the FPS drop isn't visibly noticeable, then it isn't as much of a problem (I noticed the drop down to 40FPS, and sometimes as low as 30 for short periods). After rebooting and starting Steam, Fraps and the game I got 50-60 running around a bit in the Dark Forest and 55-60 in the Cyseal marketplace, usually on the higher end of those ranges; in that case the FPS changes were not visible, except in the Fraps OSD.
My system is fairly similar to yours: Win7 Pro 64, ASUS Sabertooth Z77, Core i5 3570K, 16GB RAM, ATI HD7870, SSD for Windows/programs, HDD for games/music.