If you're in a corporate environment, it will be a Group Policy that is set by the Exchange Email Administrator.
- Right click on firstname.lastname@example.org and select Folder Permissions
- Then click on Add or Remove Retention Policies
You might get sent to Outlook for Web where you can set policies.. or nothing appears which means this is disabled by your administrator and is uneditable.
If the Folder Policy is editable, then it might give you the details of the Archive policy. It sounds like your e-mails are set to be deleted after x number of days. You can verify by seeing what is your oldest e-mail in your Sent Items.
First check why there is a deletion policy and not retention. If deletion policy is there to save disk space (bad policy), then you could try setting up your own AutoArchive to pre-empty the policy and save your e-mail to a local PST to archives emails before they are deleted.
If Group Policy affects even your local PST, then you'll have to figure out a different way to save your old e-mails.