We get the following message.  essentially what happened was.  We had a single domain certificate and search was working fine, we purchased a 5-domain certificate, we added mysite.doamin.com and docs.domain.com to the certificate and added it to the server.  Ever since then we have been getting this error. 

When I browse externally or internally the certificate is fine, I don't receive any errors.  I have a feeling SP is using the old certificate?

An unrecognized HTTP response was received when attempting to crawl this item. Verify whether the item can be accessed using your browser. ( Error from SharePoint site: WebExceptionStatus: TrustFailure The underlying connection was closed: Could not establish trust relationship for the SSL/TLS secure channel.; SearchID = 9DC4EE21-6E34-41EB-8008-5D5C3E1B9FBB )

what if you open browser on the server where search crawler is running, and put the start address in search content source (find it in search administration site) into the browser address bar.

Can you please explain clearly what do you mean ?

i have the same problem 

thanks in advance