When I click Save as Draft in the new webmail interface, I get no feedback that anything is done at all. It behaves as if the button doesn't do a thing, and since the button looks dimmer than the Send Message button, it gives the impression that it is completely broken. Closer inspection shows that the draft is being saved. Some visual assurance of this would be helpful.
A "saving message..." notice appears at the bottom status bar when I use the "save as draft" button along with a little spinning graphic meant to indicate something is being worked on. This is replaced by a bright green check and the words "message saved to drafts."
So we can reproduce the bad behavior, which browser are you using?