Fixing out-of-sync audio

I have an mp4 video/AAC audio file with out-of-sync audio. I downloaded Avidemux which has a "Shift" feature which fixes this type of problem.

I adjusted the shift until the audio was perfect and saved the file. I played the video several times in Avidemux to confirm all was well, then I quit Avidemux.

I then opened up the file in iMovie and played it. The audio was out of sync again, just like nothing had been fixed (about 300 ms).

What gives?

Ideas?

Thanks!
Dave

OS X 10.9 MaverX