You could save it to a different name then use the Replace Footage functions in AE...
Hmmm.... I'm not sure if that is specifically a CS3 problem, as I don't have an issue with it, but I'm using CS4.
Tell me if you have followed these steps in integrating Flash and AE:
1. open flash
2. create animation
3. save .fla file
4. export or hit return/enter to create .swf file
5. open AE
6. create a new comp
7. import the swf file to your project panel
8. drag the swf file to the timeline
9. hit 'spacebar' to test (or any other form of preview)
10. go back to the opened FLA file in Flash
11. make some changes
12. save the FLA
13. export a swf, or click return/enter to test the file creating a .swf
14. go back into AE
15. select the swf file that you previously imported in AE
16. right click and selete 'reload footage'
17. test your AE file again to see if it has updated the footage.
Let me know your results.