Using New Outlook on Windows for personal email, calendar, and contact management
Hi, I'm John! I will help you with this.
Can you check first in Outlook on the web here? https://outlook.live.com/mail
Sign in with the same account, then check the Drafts folder there. This will tell us if the draft is being saved to the mailbox or if the issue is only with the new Outlook app.
Also, when you create the draft, do you have more than one email account added in new Outlook? Sometimes the draft is saved under the Drafts folder of the other account if that account was selected in the From field.
Please also try this: Open new Outlook > check the left folder list > expand each account > check each Drafts folder.
If the draft is not showing on Outlook web either, please let me know if this happens with all drafts or only with one specific draft.