Not being able to save a 'session' is extremely frustrating. Please fix this Adobe!

For a start, you need to understand some basics here. Audition has two modes of working - as a destructive editor (Waveform view) and as a non-destructive editor (Multitrack view). You can record in either, but it's only Multitrack view that uses the concept of a 'session'. This is because in essence, Multitrack view is a glorified, selective, file player. If you import a file into it, you can manipulate the bits you want out of it to wherever you want them to be - and that constitutes the Session File information. But the original file isn't touched.

In Waveform view, you can manipulate the content of files directly, and when you've done whatever it is you want to them, you save them. Once you've done that, the changes to that file are permanent (which is why we always tell people to edit copies, not originals)

What a lot of people do is to make basic recordings in Waveform view, put range markers around the bits that they want to use, and then insert these into a Multitrack session, where they can be virtually 'edited' to be exactly how you want them to be. So no need to do anything to the actual recorded file at all - you just don't use the bits you don't want. Obviously you can use bits of the same file over and over again if you want - there's no limit on that. When you've got all your material assembled the way you want it in a Multitrack session, you can either mix it down, or export it. There is common ground between these options, but Exporting is rather more flexible. If you just want a mixed version of your result, then a basic mixdown is fine.

So if you open a session for your final assembly, there's nothing at all to stop you recording more mateial for it - and you don't have to make that recording in Waveform view either. Recording in Multitrack view is rather safer than doing it in Waveform view, as the results are written directly to disk. In Waveform view your recording is saved to a temp file, and not saved to your actual file until you hit the Save button. The direct to disk option always creates a file you can rescue if you need - faults in your computer's operating system won't destroy it, unlike the temp file option, which is not always recoverable, even though Audition will always attempt to.