I have a bunch of deparmental email accounts, and only one of them gives me issues not too similar to yours... mine is more that there is a lag between opening up emails/selecting emails / going to a different mailbox... but then when I go to a different mailbox it's fine.
Is the O365 account a large account (i.e. lots of calendar information, emails not deleted, etc)?
Is the O365 account a large account (i.e. lots of calendar information, emails not deleted, etc)?