This is a known issue with GoDaddy certificates, and can be corrected by specifying an intermediate cert. I ran into the same issue at one point in the past and had to Google a bit to fix it.

GoDaddy itself is not a trusted CA on all platforms. It is backed by a trusted CA. To make this work, you have to add a "certificate chain" in your web server and provide the additional certificate linking GoDaddy to that trusted CA.

Read more about the configuration here. Note that you'll have to download one additional certificate, not just the main signed certificate. http://help.godaddy.com/article/5346

Here is what my ssl.conf looks like in Apache:

   SSLCertificateFile /etc/httpd/foo.crt
   SSLCertificateKeyFile /etc/httpd/foo.key
   SSLCertificateChainFile /etc/httpd/gd_bundle.crt

That gd_bundle.crt is what you're probably missing. Hope this helps.