User creates a PowerPivot workbook with Excel, and saves it to SharePoint.
User creates a .bism file that points to the PowerPivot workbook and saves the .bism file to SharePoint.
User creates second workbook that uses the .bism file to point to the first PowerPivot workbook as a data source.
User views the workbook with Excel Services and tries to slice the data.
User gets error "An error occurred during an attempt to establish a connection to the external data source. The following connections failed to refresh."
There is a software defect that prevents .bism files from working for this use case.
Instead of creating a .bism file, create a .odc file and use that.
How to create .odc file and data connection library
This issue was fixed in CU4 for SQL Server 2012 SP2 and CU5 for SQL Server 2014: