I'm having the same problem as well with FMP 5.5v2 and Illus 10.0.3 on OS X 10.1.4. I have 1GB of RAM on a Dual 1Ghz Mac, so it's not a memory issue. It doesn't always happen and it doesn't seem to depend on the size of the elements copied in Illustrator - it happens with both small items and complex files.
Also, there is the dreaded spinning ball problem in Illustrator (when you go back into Illustrator having been in any other application). This problem seems to be a lot worse if Filemaker is open. If Illustrator hangs with the spinning ball, force quitting Filemaker sometimes stops it!
Any ideas??
Frank