I found the resolution to this issue a few weeks back and due to me being lazy I have yet to publish the full resolution on by blog. So I now have to write it up for you. Please follow the below to the letter and I guarantee it will work.

  1. Install Microsoft Office 2010 SP2. (download links towards the middle of the page)
  2. Restart if required, now remove all email profiles on the machine via the mail (32bit) utility
  3. Create a new mail profile and open Outlook
  4. When the wizard loads choose to configure a new exchange account
  5. For the server enter: outlook.office365.com
  6. Email and password should be the Office 365 email and password
  7. Click "More Settings" in the bottom right
  8. Under the Advanced tab uncheck "Download shared folders".
  9. Under the security tab, in the "Logon network security" drop-down select Anonymous Authentication.
  10. Under the 'connection' tab check "Connect to Microsoft Exchange using HTTP".
  11. Click "Exchange Proxy Settings" use the URL: outlook.office365.com
  12. Tick "Only connect to proxy servers that have this principal name in their certificate" and enter: msstd:outlook.com (Please be aware that there's a typo in the screenshot below; the description here is correct.)
  13. Check both the checkboxes
  14. Under "proxy authentication settings" drop down select "Basic Authentication".

Now reload Outlook and sign in at the first prompt. Be sure to check "Remember password".

Screenshots for reference:

Answer from Samuel Nicholson on Stack Exchange
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Microsoft Support
support.microsoft.com › en-us › office › how-to-sign-in-to-outlook-on-the-web-763fab4d-0138-4814-b450-37fc286bcb79
How to sign in to Outlook on the web - Microsoft Support
If you successfully signed in, but not sure what you're signed in with, select the Account manager in Outlook. If you're not signed in with the account you want, select Sign out and start the process again, or select Sign in with a different account and follow the prompts using the correct account. Go to login.partner.microsoftonline.cn and sign in with your work or school account username and existing password.
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one.com
help.one.com › hc › en-us › articles › 115005594505-Setting-up-Microsoft-Outlook-2010
Setting up Microsoft Outlook 2010 – Support | one.com
Open Outlook and select File. Click Add Account. Check Manually configure server settings or additional server types Click Next Select Internet E-mail Click Next ...
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InMotion Hosting
inmotionhosting.com › inmotion hosting home › support › email › outlook › outlook 2010: accessing account settings
Outlook 2010: Accessing Account Settings | InMotion Hosting
August 17, 2021 - Once you have Outlook 2010 open, click on the “file” tab on the top left labeled “File“: Then, select “account settings” as highlighted in the screenshot below and click on the popup box: Now, you will see all the email accounts you have set up in Outlook. Double-click on the account you wish to view the account settings for: On this following screenshot you can edit your incoming and outgoing servers, email address and login ...
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Amancorp
amancorp.com › hostgcc › knowledgebase › 160 › Setting-up-Email-Account-with-Outlook-2010.html
Setting up Email Account with Outlook 2010 - Knowledgebase - Aman Corp
Microsoft Office Outlook 2010 Login screen · You will complete the following: Open Outlook 2010 · Create a POP3 email address · Enter your email settings · Send and Receive email using Outlook 2010 · Have the following ready before you start: Your domain name.
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Microsoft Learn
learn.microsoft.com › en-us › answers › questions › 4683679 › email-access-from-outlook-2010
Email access from Outlook 2010 - Microsoft Q&A
I would prefer that you use New Outlook to add your email account, (it's a free application) as the Outlook 2010 application is just too old.
Find elsewhere
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O'Brien Media
obrienmedia.co.uk › home › configure microsoft outlook 2010 to access your email account
Configure Microsoft Outlook 2010 to access your email account • O'Brien Media Website Design and Support
September 5, 2024 - Knowledge Base Email Software and Settings Configure Microsoft Outlook 2010 to access your email account
Price   $$$
Address   Suite 4, Marlborough House, 26 High Street, Old Town, SN1 3EP, Swindon
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HostGator
hostgator.com › help › article › email-setup-for-outlook-2010
Email Setup for Outlook 2010
This article will walk you through setting up an email account in Outlook 2010.
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Reddit
reddit.com › r/sysadmin › outlook 2010 connection to microsoft 365
r/sysadmin on Reddit: Outlook 2010 Connection to Microsoft 365
July 2, 2021 -

Let me preface this by saying, yes, im aware just about everything this client is doing is out dated and a huge security flaw, not supported by MS, etc etc....

Still need to try and see if i can get it fixed though.

They are on exchange online plan 1, connecting to their mailboxes using Outlook 2010 (as up to date as possible as far as i can tell)

No one can give a straight answer as to when things began, but users are starting to be prompted for their passwords, where they used to not be.

They are getting stuck on "unable to connect to server" until they restart their machines.

They are all using Server 2008R2 Terminal servers as well.

again, I'm aware they need to update a LOT of their stuff, but i can only work with what I'm given and approved to do.

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Microsoft Learn
learn.microsoft.com › en-us › answers › questions › 4678533 › outlook-2010-and-gmail-cant-log-in-after-password
Outlook 2010 and Gmail - Can't log in after password change - Microsoft Q&A
If the above does not solve the problem, then you need to contact your Gmail service provider to see if they can help you to continue using your Gmail account on Outlook 2010, as the main reason for this issue is that Gmail has disabled your ability to use the “low security “ authentication method on Outlook 2010.
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Intermedia
support.intermedia.com › app › articles › detail › a_id › 10133 › ~ › how-do-i-manually-connect-microsoft-outlook-2010 › 2013-to-my-exchange-server?
How Do I Manually Connect Microsoft Outlook 2010/2013 To My Exchange Server?
Enter your administrator login credentials to access the $cpanelfirstuse and follow the instructions to obtain the server information. Type your Exchange Mailbox Username (email address). For the Offline use option, make sure that Use Cached Exchange Mode is selected. Click the More Settings button and switch to Connection tab. In Outlook 2013 you can specify the time period for which email items will be kept offline.
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Super User
superuser.com › questions › 326889 › microsoft-outlook-2010-forgets-login-details
Microsoft Outlook 2010 Forgets Login Details - Super User
Microsoft Outlook is running in the background and constantly pops up the following dialog: Even when checking the check box it does not persist! I am using a POP account and not Microsoft Exchange...
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Reddit
reddit.com › r/sysadmin › outlook 2010 constantly asking the user to login in
r/sysadmin on Reddit: Outlook 2010 constantly asking the user to login in
June 2, 2015 -

Hey guys, I've just had the CEO of our company shouting at me on the phone: it's this weird bug where outlook doesn't remember her login credentials. It works fine for 2-5 minutes, but then the login menu pops up again. I've tried checking credentials manager, but it doesn't show any details about Office. Maybe I need to do it in the admin account? There are 2 or 3 other users in the company (of around 150+) who are having this issue. I'm completely out of ideas.. and yes, I'm ticking the 'remember' button :s


Thanks for all the help guys! I'm going to try it out soon, will keep you all posted. SO MUCH APPRECIATION!

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Microsoft Support
support.microsoft.com › en-us › office › get-help-and-support-for-outlook-2010-df1ceeb5-075f-4ec1-ade8-8893c35731bd
Get help and support for Outlook 2010 - Microsoft Support
Get help with Outlook 2010 features, ask support questions and review solutions from other Outlook users, or contact a Microsoft support professional.
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Bluehost
bluehost.com › help center › email client › email application setup outlook 2010 for windows
Email Application Setup Outlook 2010 for Windows
This guide provides instructions for setting up email in Outlook 2010 for Windows, aiming for efficient communication. The steps are designed to be clear and helpful for anyone, whether for professional or personal use. By following this guide, users can effectively utilize Outlook 2010's features for their email management needs.