The draft folder doesn't sync and can't be forced to sync. It's a limitation of the EAS account.
Instead of connecting your Outlook.com account via the EAS protocol, you could configure it as an IMAP account. BUT! While it does support synching the Drafts folder, the IMAP protocol doesn’t support a whole lot of other features such as Flag Reminders, Categories or synching Contacts, Calendar and Tasks Folders.
Yet another workaround would be to drag and drop the message out of Outlook and into your OneDrive or Dropbox folder. This will create a copy of the draft message in the msg-format which you can finish on another computer that also synchs with that OneDrive or Dropbox account and uses Outlook. The downside of this method is that the message won’t be available in your Outlook.com mailbox online and that it only works with Outlook since the message is stored in the msg-format.