Looking at the Technical System templates both ABAP 7.00-7.03 & 7.10 and higher both look for /sap/public/ping for the HTTP availability. In tx SICF do you have this activated?
If this is a Instance template, and Instance Local Http Availability is being used, its still looking to the same /sap/public/ping location.
Do you have ACLs or a firewall that may be blocking the GET requests from SolMan? From the SolMan system can you pull up a browser and see what the HTTP return value is for this ABAP system, this would tell you if its a infrastructure (acl/firewall) or something in the templates as being the issue.