I've been having this problem with MythTV recordings for quite some time. The MPEG headers contain an audio delay value which is often quite large - almost 1 second on Australian broadcasts. These can be seen using the program 'mediainfo'.
I checked a file with mediainfo, and it returned a delay of -456ms. When the same file is opened with avidemux, the A/V sync is set to 0ms, and the audio is out of sync when the video is played or saved. When I manually set the sync value to -456ms, the a/v sync is perfect.
AviDemux needs to automatically read the A/V sync value from the MPEG header when a file is opened.
The recordings I am using are from MythTV on Mythbuntu 9.10, from an Australian PAL DVB-T broadcast. The audio sync is usually OK when a file is played through another program, and the delay value is definitely embedded in the header.