After fighting with this issue for over two years I think I finally have the answer for me at least. I host with ixwebhosting and I called them to help me work through this. Although they do not support zen they are very helpful.
On thing I did drill down to is that my no email problem seemed to happen when I did a large emailing from within zen. Let me say this did not cause a blacklist problem, I checked. However, for some reason it seems to be a connection there. Maybe some zen gurus can see if there is something to it.
Anyway, They explained how each method works and since I am on a linux server we went with sendmail option. All seems well for now.
Does it make sense to say that it really isn't the host error when you can still send emails outside of the zen program?