If you receive an 'SMTP Client Error' something like:
451 (firstname.lastname@example.org) Sender Domain Must Resolve
this means that the ISP's mail server cannot find the domain.com part of the email address.
Often this means that the FROM address of the message is invalid, or that the
Settings → Local Mail → Default Domain is incorrect. This setting should always be a valid Internet email domain.
Occasionally this can happen if you have just registered a new domain (or moved the domain to a new ISP) as the DNS entries for the domain can take a while to propagate to all DNS servers, so the mail server may be talking to a DNS server which doesn't recognise the name yet - in this case waiting a few hours may cause the problem to rectify itself automatically.
If you know that the FROM addresses you are using are correct, try contacting the ISP to get them to check their settings - it is not unknown for their servers to be set up incorrectly.