If you are a Domain Administrator login to the domain the Mailing List is on and go to SETTINGS > DOMAIN SETTINGS > GENERAL SETTINGS. Click on the MAILING LISTS tab and set the DELETION BOUNCE THRESHOLD setting to the desired setting or remove the checkmark next to ENABLED (the later option is not recommended if this is a Mailing List that sends to external email accounts).

 

When an email bounces back to the Mailing List multiple times and exceeds the setting in the Deletion Bounce Threshold they are automatically removed from the Mailing List. This is to ensure that only good recipients are retained on your Mailing List and to prevent your Mailing List (and Mail Server) from being listed on RBLs or reported for Abusive behavior. Again, if this is an internal only Mailing List then it is certainly okay to disable Deletion Bounce Threshold, especially if you have local users who routinely have their mailboxes full. 

To add to what Scarab stated, if you do not remove bounced and non-deliverable e-mail addresses from a mailing list you are in violation of the US Can Spam Act, the EU Can Spam Act, the Canadian Can Spam Act and the Australian Can Spam Act.

 

Here's a link to the

 

US Can Spam Act: https://portal.chicagonettech.com/kb/a28/can-spam-act-us.aspx,

 

EU Privacy and Electronic Communications (EC Directive) Regulations 2003

 

Australia: Spam Act 2003 

 

Canada: Canada's Anti-Spam Legislation (CASL) - and Canada made their laws a LOT TOUGHER in January, 2015.  Example:  If you send to any BLACKBERRY DEVICE, and the device uses Blackberry's SMTP SERVERS in Vancouver, BC, Canada, which almost all of them do, even if they are used by a US based company, with a US based MX server and US hosted domain, you must comply with the Canadian Can Anti-Spam Legislation (CASL).

 

You will also need to make certain that you have followed the Opt-In Laws in North America and Europe - to the letter.  The EU, Canada, and Australia, have all been very aggressive in prosecuting those who do not abide by these laws, leveling some pretty hefty fines against violators.

 

You will also be, most likely, permanently, blocked by YAHOO, GMAIL, OUTLOOK.COM, AOL, and COMCAST as you will also be a spammer.  That will get you listed in RBLs, and blocked by everyone else.