I have a similar problem. For at least a year I've been able to access my email using Outlook on my laptap and also using Android clients on my phone and tablet (both Samsung). Using IMAP I've been able to sync all me emails across these devices. Over the past few weeks this capability has become very intermittant. What happens is that Outlook reports a Send/Receive Error (0x800CCC0E) "cannot connect to server". New emails are not download, emails in the Outbox are not sent and no other folders are sync'd. On the phone and tablet, the sync just fails with same results. What has happened up to now is that sometime later (hours) everything starts working again, but this time I've been unable to sync for over 12 hours have stopped and restarted Outlook and the laptaop several times. I've checked all the port settings, passwords etc and they all correct. Nothing at my end has changed. The only common factor is BT mail and my 'login' .
Don't change anything, nor remove/add account to devices etc.
I suggest turning off auto polling of emails in the devices if set to check every few minutes. Do a manual check every hour or so on one device and hope the system wakes up. This fault has been known to last from a few hours to a few days.
The fault is unknown, but if more than one device is trying to sync at the same time, it may cause system confusion - even a lockout timer.