If the audio of the avi is at a frequency OTHER than 48khz, it will (sometimes) go out of sync during encoding.
In order to get your burns in sync, you should be using better tools, and do audio and video separately.
I know Nerovision Express is a nice, "one-click" solution to dvd making, but it's far from the best.
If you want to take making dvdr's seriously, I recommend you get used to using separate applications for the various steps.
Rip the audio from the avi in virtualdub, audio setting set to Full Processing. Click File, save wav, and save it somewhere. Takes about 2 minutes.
Encode your video with no audio, in your favourite encoder, tmpgenc, Mainconcept, Canopus, CCE, QuEnc, whatever.
Transcode audio to 48khz AC3 using Ffmpeggui (it's free).
Author the dvd in a good app like DVDLab.
If you find that's too confusing, be prepared to have OOS audio. Nero's audio encoder is not the best.
If you just want the movie onto dvd, try VSO Divx to DVD (it's free), and does a better job of encoding than Nero, but no menus.