Audition exporting silent files

Since you haven't told or shown us exactly how you've set this up - or even whether you're running on a Mac or a PC, we can't tell you what you've done wrong. And that will be the case; you'll have a configuration error somewhere. If that wasn't the case, then everybody would be complaining about it, and they aren't.

In multitrack view, there are a number of possibilities. The most common one is that either track outputs, or indeed the Master output, are incorrectly routed. With the Master output, if you have the output set to none, then even though you won't hear anything, the meters will still give you an apparent output - but you'll get a silent file. To check the status of everything, it's easiest to use the Mixer tab; the errors are relatively easy to spot there, as a rule.