I don't have this player, but it's possible that this player doesn't handle divx/xvid files where the audio is encoded with variable bit rate (VBR) instead of constant bit rate (CBR) very well.
Do you know what type of audio (MP3? AC3?) and bit rate encoding type (VBR or CBR) is used in the files where the audio goes out of sync? If you aren't sure you can use a tool like GSpot or MediaInfo to find out.
If you are familiar with audio and video encoding tools, try this - demux the audio from the video file using a tool like VirtualDubMod. You choose Streams > Stream List from VDubMod's menu, highlight the audio track in the dialog box that appears and click the "Demux" button. Save the audio file where you will find it again.
Then use the audio encoder of your choice to transcode the audio to CBR MP3 (there are free ones out there if you don't have one).
Remux the new audio file with the original video file using VirtualDubMod again. When you remux the audio, you will choose Stream>Stream List from VDubMod's menu and disable the original audio stream in the file by highlighting it and clicking the Disable button. Then click the add button and choose the CBR mp3 file you created. Click OK when you are done.
Save the file under a new name using "direct stream copy" as the video mode so the video isn't re-encoded. The whole process should take just a few minutes.
Copy the new video file to your USB stick and see how audio playback is.