Adobe Premiere won't update audios
I would try deleting the cache around time in your sequence causing trouble. You can mark an In and Out point, then clear the cache between those to points using &quot;Delete Render Files In to Out&quot; in the Sequence menu.
You don't necessarily have to delete all of the cache (although try that if nothing else works).
These are the steps I would normally take to do what you're doing:

Import an audio file in Premiere and place it in a sequence.
Right click on the clip in the sequence and choose Edit Clip in Adobe Audition
Edit the audio file in adobe
Save in adobe
The updated audio should appear in Premiere after a few seconds

Premiere sometimes needs to convert your file before it sends it over to Audition, so you might be modifying the wrong file in Audition without realising it if you're doing it all manually instead of letting Premiere manage it.