KB01120807 What is the error 'Too many concurrent connections from one IP address' ?
This error can occur when sending outbound email via your ISP's mailserver (commonly known as a smarthost).
The problem is that some ISP's limit the number of simultaneous connections they will accept from an individual machine (they do this to avoid being swamped by misconfigured machines or denial-of-service attacks).
To solve the problem, in Options | Outgoing Mail | Delivery Options tab, reduce the value in 'Maximum number of parallel delivery connections' until you no longer get those messages.The default value of 10 normally provides a fast service, as mail held up by one system does not delay other messages, however a lower value can prevent the ISP from blocking your mail.
As an alternative, you might consider sending all your mail out via MX lookup. That avoids the bottleneck of ISP smarthosts completely. See Sending Mail without a Smart Host for information on how to do this.