In the sent email list, the user could not find some old emails.
The Sent Email feature provides similar capabilities as the Undelivered Emails feature. However, Sent Email also provides information about all outbound email sent from an account. However, the list contains search results from the previous 100 days of activity.
So, if the email is sent before 100 days from today, then it will not show in the list also in the saved search of the same.