I just tried it, and it does NOT happen to me.  I'm using Chrome.  When I go back to my draft (here in this group), it's there and its contents are there.

I have not tried Firefox, and won't.

One thing to be aware of - probably unrelated - is that the menu bar on the left does not always refresh, so I may need to do a complete screen reset occasionally.  But I think that only affects the presence (and number) of Drafts that it tells you you have.  e.g., I may write a message, so now there's a new Draft, but it doesn't show up in the menu bar on the left until I refresh the browser's screen.

Andy