When it works and then stops working it is very likely that a change happened at your host. It is possible, for example, that your host removed or moved the "/usr/bin/wget" program used by the ListMailPRO cron task. It is also possible that SMTP was changed... Can you get test emails to your lists out using SMTP? PHP mail() is used for welcome, confirmation, and some notification emails (such as the dailymail report) - can you receive welcome and/or confirmation messages ok?
Regards, DW