The problem is the shared SSL. Setting it up again will not make the issue go away. If you were using a dedicated SSL on the other hand, then this issue goes away. I believe that in general the knowledgeable Zen Cart gurus do NOT recommend using a shared SSL certificate.
One last thing on the shared SSL certificate tip, if you have ANY plans to use any kind of friendly URL add-on (Ceon URI for example) you will NOT be able to use a shared SSL certificate.
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