To export 5.1 audio, you need the Minnetonka Surcode plug-in. You have three tries before you need to buy it.
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Harm has given you the reason for the Stereo in the output.
Now, I do not use Soundbooth, but one can easily edit 6-channel (most often seen as 5.1) Audio in Audition, BUT then to output to something that will contain all of those channels, one must choose such an output, say WMA. However, that will limit the uses, i.e. no DVD/BD directly. One MUST use an Encoder, such as the SurCode, to produce a DD 5.1 SS AC3 for the primary Audio stream in DVD/BD (or as a supplemental Audio stream, if one has done a 2-channel primary), or they can do something like DTS, but that can ONLY be a supplemental Audio stream in DVD/BD.
For Encoders, one can easily use the Minnetonka Audio SurCode plug-in for PrPro, a SurCode, or similar, stand-alone Encoder, or stand-alone DTS (fill in any other DVD/BD compliant supplemental Aduio stream here) Encoder.
PS - for DVD/BD, there are only two types of Audio steam allowed for the primary stream - PCM/WAV, or DD 5.1 SS AC3. Supplemental Audio streams are a bit more open, though most will be player dependent. If you do DTS, for instance, your client might, or might not, be able to fully appreciate that.