I have the same problem and this explanation does not apply. The issue I am also having is that when you have a draft you are working on, it does NOT save to drafts even with save drafts is on.
INSTEAD, it stays in an email conversation thread. This is a ridiculous design flaw and I would love to know how to correct the settings to allow for ALL drafts regardless of where you start them, to ALWAYS save in Drafts. From what I can see, some developer got a little too cute with coding and failed to actually attempt to use their design.
Please provide a real answer to fix this that doesn't have 300 steps.