I had seen this issue before but found another cause for it today.
In this case, the client was using SCCM (System Center Configuration Manager) and couldn't access reports from the reporting server. After resolving some other issues, I was left with "The underlying connection was closed: Could not establish trust relationship for the SSL/TLS secure channel" when I tried to go to http://servername/reports.
When I've seen this previously, it's been to do with the trust relationship between a pair of servers. However, I hadn't seen it come up before on a single server.
When I checked the SSL bindings in Reporting Services Configuration Manager, in the Advanced tab, I found that no certificate was associated with the SSL configuration. When I tried to edit it, and choose the cert from the dropdown list, the certificate binding could not be applied. (It would be useful if it told you why at that point). That had me puzzled until I opened Report Manager in IE and viewed the certificate. The certificate had been generated onsite and had expired.
Hope this helps someone. (Or helps me the next time I see it and can't recall what it was :-))