You have to configure your phpBB script to send less than 400 messages per hour and every message should be addressed to no more than 40 recipients. By default the forum's Mass Email feature is configured to send the email to 50 recipients at once. In order to resolve the issue you need to edit the following phpBB file:

includes/acp/acp_email.php

and change this code from:

$max_chunk_size = 50;

to

$max_chunk_size = 30;

After that, your phpBB forum will be in compliance with our e-mail terms and all messages should be delivered just fine.