Did you use an MP3 file in the edit? If so, convert it to AIFF first (match the sample rate to your timeline -- standard is 48kHz), then recut the AIFF version into the timeline, delete the MP3, and then try again.
Are you using Export - QuickTime Movie? Export - Using QuickTime Conversion will result in loss of quality.
What is your Scratch Disk? Make sure there's enough room on all drives connected to the computer (at least 10 per cent free, plus sufficient room for the QuickTime export on the target disk). Don't export to the system drive.
Does the dropout occur at the same point every time on the QuickTime movie file?