As a follow up to my post Deleting old emails in Gmail 3 years ago, I’ve now found a way to automatically delete old emails from Gmail.
This trick uses the rather unknown Google Scripts, a Javascript engine which runs on Googles servers.

• Pop to Gmail and test some searches, eg label:webserver older_than:1m this will find all emails labelled webserver and are older than 1 month (full list of search options here.
• Once you are happy that your search result has found the emails you don’t want, go to script.google.com.
• Select Create script for GMail
• Delete all the example code
• Enter this code
  function deleteOldEmails() {
var threads = GmailApp.search('label:webserver older_than:1m');
GmailApp.moveThreadsToTrash(threads);
}
  ensuring you replace label:webserver older_than:1m with your search phrase
• Save you project
• Press run
• Once the notification at the top has gone, check back in Gmail to confirm your emails have been deleted.
• To automate, click on the Clock icon, Add a new trigger. Select your function, you want it Time-driven, and for me I’ve selected Month timer, 1, Midnight to 1:00am

The result will be on the first of every month Gmail deletes all emails older than 1 month from my webserver folder.