Mailman will stop sending mail to addresses that exceed a certain number of "bounces" (returned mail errors) within a certain period of time. There is some forgiveness built into this system to allow for things like full mailboxes or temporary server outages, so a "bounce action notification" (where Mailman sets an address to "nomail") usually means that the address in question is no good.

See http://lists.uua.org/mailman/admin/listname/bounce ("Bounce processing") for more information. The default settings on this page should be fine.

See "Enabling / Disabling Mail Delivery" for more information about verifying and/or reinstating a member's mail delivery status.