Outlook keeps asking for a password and I have deleted the profile but it still shows in my email profiles

Do you use 3-factor authorization? Outlook wont ask for the 2nd factor for provides - you need to use the app password instead.

What type of email account was it? POP, IMAP, Outlook.com, or Microsoft Exchange?

POP data files are left in the folder list, they need to be removed from the File, Account Settings - under the Data Files tab.

How many accounts are in your profile? (It might be easier to make new profile.)

I was advised by the Microsoft help line to add the 2 factor authorisation on my account which was a nightmare but done. It is applicable to my account email and I entered the app password for that email address, but the other email address which is the Microsoft Exchange account keeps asking for the password still, even though my other 2 Microsoft Exchange passwords do not. It asks for a password whenever a mail is received on the account which is often. I tried to remove the email address so I can at least function but although it removes it in the account settings it does not remove it from Outlook. I have tried right clicking on the email address and saying close the email but it says I can't do that and that I need to remove it via account settings which I have done.

Regarding the profile option are you suggesting that I create a new profile and add the email addresses I want there and then can I delete the old profile where this address had been? Will that cause any problems and will I have to download all the emails attached to the accounts again?

Just don't understand how this happened as all was fine up until the update to Office 365 this week.

If it was fine until the update, and you subsequently didnt change anything, then in the first instance repair Office

I have run the repair on Office, both the quick one and online one and problem still occurs

Since the update of the Office 365 earlier this month, I have had constant problems with the Windows Credential Manager calling for a password repeatedly. I have removed all the retained passwords here. To note that none of the passwords have been changed anyway since adding the email profiles so not sure why this should happen as the retained password in the credentials manager is much longer than the one the account has always had.

I have several emails attached to my Outlook, and it was particularly troublesome with the one profile, which I decided to delete. 

I have deleted it via the File>Account Settings and is no longer listed there, however it still appears in the listing in the left panel of  Outlook AND it is still receiving mails, although it is nowhere in my account settings lists.

Anyone have any ideas for me?

My issue has been resolved. It appears that there was a historic setting on the Hosted Exchange platform that was creating the problem and the service provider has removed this and I have been able to delete the mailbox.

Thank you to those who did try and assist