Since upgrading to Snow Leopard and restoring Apple Java 1.5.1 from backup I've been having tons of stability issues with IntelliJ 8.1.3 and I finally got this resolved today. It seems that there is a reason why Apple chose to remove their 1.5.1 version from Snow Leopard after all. I think there are some compatibility issues with the new OS version.
Since modifying IntelliJ's startup configuration to use Java 1.6 instead of 1.5 and clearing out the old caches, all the stability issues seem to have gone away.
I modified /Applications/IntelliJ IDEA 8.1.app/Contents/Info.plist as follows: