Sending, receiving, and organizing email in Outlook.com
It states that in Classic Outlook for Windows, a delayed message remains in your Outbox, and Outlook must be connected and online for the message to be delivered.
I suggest that you use Outlook in a web browser for now(or the New Outlook App). Here's a quick path how to do it.
New message → arrow/drop-down beside Send → Schedule send → choose the date and time → Send.
The message should remain in Drafts until the scheduled time and then be sent by the servers, you shouldn't have to keep the browser open or stay logged in.