Purely a guess on my part but does setting the mp3 to 48kHz, rather than 44.1, help?  My thinking is that your camera is almost certainly recording audio at 48kHz but your mp3, at 44.1kHz, will be as it were "truncated" and hence it is, effectively, running "faster" than your video.

Also, depending on various parameters like the codec being used, there are other threads on these forums about problems that avi files can have, given that "avi" is merely a container which can include a variety of contents.

If I have the chance later this afternoon I will atempt to duplicate what you are doing and see if I get the same result.

Jeff

UPDATE: I did test this on my VPX5: I "exported as avi" a 13 minute section of a DV AVI video.  Once completed, I placed the exported version directly below the original on the timeline; by the end of the export, the video was approximately half a frame behind the original, with the audio a further half-frame "late", not perfect but certainly not a delay like you are seeing of "more than 1 second".  So I really don't know what to suggest!

However, never having used the "export as avi" option before I was concerned to see the "default" audio setting is as you state in your post. mp3, 128kB/s, 44.1kHz, with no apparent way to change any of those settings!

Just for experimental purposes I also chose to "Export audio as mp3", using those same settings, and then reimported this new audio file to the timeline.  The results were exactly the same, approximately a 1 frame difference after about 13 minutes. (I checked this by referencing the graphics of the audio on the original file with those of the exported mp3.)