I've done some googling on this and haven't found anything that exactly matches my problem, so thought I'd try here...
I have two personal email addresses - xtra and gmail. As I have an Office365 account, I created an @outlook.co.nz email account and linked my two accounts to it - the xtra account set up using POP3 and the gmail account using IMAP. For about a year this has worked fine. I pick up all my emails through the Outlook apps on my Windows 10 notebook or Android phone, or through outlook.live.com/owa online. I know I still have to go to Yahoo/XTRA or Gmail to delete the emails there, and I do this every few weeks, but if I delete an email in Outlook on one device and empty the Deleted Items folder, I don't see the message when I open Outlook on another device.
While I was away over the weekend I got a message from Outlook saying:
Please update your credentials for the account [xxx]@gmail.com.
It looks like we don't have permission to get mail for [xxx]@gmail.com.
Our last successful sync was at [a date and time about two hours before the message was sent].
It gave brief instructions on how to fix it - basically just to go to Settings on Outlook.com, select Connected accounts and "follow the instructions onscreen". This ended up with me deleting the gmail account and adding it again. Now, whenever I delete an email in one of the Outlook apps, it stays deleted if it's from the xtra address but reappears a couple of minutes later if it's from the gmail address. It doesn't matter how many times I delete an email, it reappears until I go to Gmail and delete it there.
I note that in the settings on Outlook.com under Accounts > POP and IMAP there is an option for POP settings that says Devices and apps that use POP can be set to delete messages from Outlook after download and this is set to Let apps and devices delete messages from Outlook.
My theory is that if I can find a similar option for IMAP it should solve my problem, but I can't seem to find it anywhere. Any ideas?