FYI - I have tracked this problem down to being related to the other issue I am experiencing on my site.

My host has somehow made some change affecting the mail transfer on the server. I am setup to use smtpauth (php is not an option as I am not running the most recent version(s) of zencart).

Whatever the host did has made it so my shop cannot connect the smtp host - for some reason, this prevented the order confirmations from being generated at all.