I would think an 8600 GT should have no problem with 2 sessions, I used to run 2 on less of a card than that no problem. Something else must be wrong. If you're on XP, did you recently add a monitor? There's a known issue with bad frame rates on multiple monitors in XP. Otherwise, I'd have a look at your task manager and see if there's any process that's eating up a large amount of CPU time (other than WoW of course). A good virus scan would also be a good idea if you haven't done that recently to make sure there's nothing malicious going on.

Another possibility is that your CPU fan or heat sink is clogged with dust and not cooling properly or the heat sink is not properly installed. Pentium 4 and above chips will automatically slow themselves down if they start to overheat to prevent them from burning themselves up. Once after taking off my heat sink to clean it, I failed to reinstall it properly and my computer's performance dropped dramatically until I realized what was wrong and fixed it. If your motherboard maker has any CPU temperature monitoring tools, it might be worth checking that too. The normal range depends on your chip, but I think about 70C is where most of them start to slow down.