Hi Colin,
There may be limitations per hour or day. Does the message on the first list -always- get sent when you test it, then the 2nd+ lists don't work, then the first list (tried again) works?
Can you see anything different on the lists that work and the list(s) that don't? Could the "Send From Email", perhaps, be different on lists 2+? Some hosts have a rare restriction that the "Send From Email" must exist in your web host control panel either as a forwarder or an actual mailbox.
Do you have a subject and text copy of the message entered? These are both required, even when sending HTML email (in that case I recommend a message code of the type "Link to HTML" be used as your text message)
Please let me know if I can be of further assistance!
Regards