Greetings,
After many emails to 1&1 tech support and my own experience (fsockopen: connection could not be made) it is clear that they are blocking connections from the web server to the SMTP host on both ports 25 and 587. ListMail does support SMTP authorization - it works with practically -every- other host and
used to work on 1&1. Now, however, it appears 1&1 has a new policy in place to prevent connections to SMTP made from scripts on their web servers. This can be implemented with a local firewall or other IP-based rule.
If you ask or phone 1&1 tech support they will claim a problem with the script, port, etc., but they are wrong. Apart from the new SMTP restriction I am very happy with 1&1s web services - they're top notch (I rent a few dedicated servers from them and their panel is excellent for self-recovery) However I am quite dissatisfied with their support - even with all of the details and a clear technical explanation they can't give a straight-up answer.
Big hosts aren't always better - often they have more restrictions and poorer deliverability due to placing large numbers of users on each server.
If you don't want to switch hosts (
reviewed here) you may have to switch to the alternate mailing method "internal PHP mail".
Regards