Thanks for the response. I am actually using GoDaddy's smtp servers. The messages were not just test messages, but every "normal" message I sent to the client.
As it turns out, however, the problem has been resolved. It was at the client's end. Apparently, their mail system has a somewhat hidden option to remove spam "instantly" instead of placing it in a folder. Somehow one of my messages had been seen as spam, which marked all subsequent messages from my domain as such. The messages were being instantly deleted, so the client never saw them in their spam folder.
<homer> DOH! </homer>
Thanks for the help!