we can't complete this because we can't contact the server right now

I'm not precisely responding to Kyle McGovern but sharing this with anyone else still experiencing this issue. Although this is a very old post (from 6 years ago), I stumbled across it because I was experiencing the exact same error message and had 3 emails stuck in my Outbox. This is what I did to resolve this issue:
-- Exit MS Outlook
-- Exit MS Teams (just in case you have a version that is tied to Outlook as a mail-enabled item)
-- Launch Windows (File) Explorer
-- Navigate to C:\Program Files\Microsoft Office\root\Office16 (for MS O365 suite)
-- Single Click inside of that folder on any file/item and tap the letter 'S' key on your keyboard twice
-- You should see the SCANPST application
-- Double-click on SCANPST and a MS Outlook Inbox Repair dialog box will appear
-- The file name to repair should automatically appear there. But if not, then browse to 'C:\Users\Profile\AppData\Local\Microsoft\Outlook\email address removed for privacy reasons'
-- Click Start. It may ask you to overwrite that existing file with the same name. Click Yes to Overwrite.
-- Allow this utility to run until it reports that it's completed
-- Launch MS Outlook and see if those messages stuck in the Outbox have been sent automatically or try pushing them out by hitting "Send and Receive".

I have had the same problem.

• Webmail was fine, so no licensing issue
• Using Monthly Channel (targeted) Version 1801 (Build 9001.2122 Click-to-Run)
• Outlook would prompt repeatedly for passwords.
  • Removed my profile
  • Could not create a new profile (something went wrong...)
• Ran Recovery Assistant (no errors found!?) and that created a new profile. 
• Outlook managed to connect and rebuild the OST
• Shortly after, Outlook started prompting for passwords again.
• Removed the profile again
• used Credential Manager and cleared the outlook credentials
• Tried to setup a new profile using outlook and the mail applet i Control Panel but that failed.
• Used the Recovery Assistant to do its checks which again was no errors found but it again created a profile.
• Started Outlook and it rebuilt the OST. I am now connected and have had no prompts for password for 10 minutes. Crossing my fingers here..