Office 365 email extremely slow

Dear all,

From time to time we have a Office 365 mailbox (90% full) that is shared by multiple people that gets really really slow, sometimes very hard to connect (we are using the web browser, not outlook)

I think the issue comes when someone tries to do a big cleaning, 7 GB today and maybe the sync causes disconnections? any ideas? We tried several approaches but cant find the reason of the issue