It let's you save. I just tried it. Your problem is probably that the export-window is too large and so you can not see the save-button. I had the same issue the first time I tried it, but now - after doing it again - the window is shown completely. No idea what made the change. But the first time I exported, I had to do this:
- recorded my voice
- go to file->export (the window will be too large to show everything)
- enter a filename and choose the path you want to save to
- move the window either by holding the left-shoulder-button and using the touchscreen (click and drag) or by doing the following key-sequence: press "fn", then press and hold "alt", press "7" and release "alt", then move the window with dpad. In the lower right corner is the save-button and the button to choose the format (choose e.g. "mp3").
By default it will save to your appdata-folder of audacity. And as already said, I only had to do the resizing ones.