The search request was unable to connect to the Search Service.

This is an error I faced trying to set up a fast search centre in an OOTB environment.

TechNet provides four common causes for this issue.

1: The communication channels are not cleaned up correctly
2: The FAST Search Server 2010 for SharePoint query processing services are not running
3: The SharePoint certificate is not present on one or more of the FAST Search Server 2010 for SharePoint query processing servers
4: SharePoint has not been configured to point to the FAST Search Server 2010 for SharePoint query processing node

Reference: Technet