Why does recent mail disappear from imac and iphone, while remaining on macbook?

Question

macOS

dd.
The situation is the following. There is a poppy beech (old), a poppy beech (a little fresher), an imak (the latest) and an iphone.
On poppy and macbooks, Outlook (2011 and 2016) is used as an email client, on the iPhone, a standard mail application.
Mail settings on all poppies are the same, because. migrated from the old to the new. The iPhone was set up manually.
The situation itself.
Old letters (older than a week or two) from the inbox disappear without a trace from the iMac (Outlook 2016) and from the iphone. Physically, the user does not delete them. Letters are lost, sometimes in whole chains. At the same time, they remain on both MacBooks (Outlook 2011). These letters also disappear from the mail server. The mail server on its own domain, mail has been spinning there for 8 years, without restrictions on the inbox.
At the same time, VERY old letters (2-3 months) remain everywhere.
Actually, the question is about the situation, where do the letters go and how to make them so that they do not disappear?