If Airmail does not update your emails such as outdated search result, loading messages or folders, you have a solution to update the database manually.
To resolve such a problem, go to 'Preferences > Accounts > Select an Account > More' and under 'More' tab there is an option named 'Clean Message Cache' . Its beside 'Reset' as shown in the screenshot below:
After clicking on 'Clean Message Cache' there’ll be a dropdown window and clicking 'Rebuild' will allow you to rebuild database for a particular account as illustrated here under:
When it’s done cleaning, your mails will be downloaded again afresh to the new database and all outdated contents/discrepancies will be cleared as well.
NOTE: Rebuilding for POP accounts is not recommended. Because the database will be cleaned and re-downloaded from the server and the current database will be lost.