SSIS 2012 Project Connection Manager does not expose ServerName property for configuration in SSMS 2012

We have deployed one SSIS 2012 project with two ADO.Net Project Connection Managers. (There are five packages within the project.) The project has a related Environment, with a variable containing a server name. I want to map the variable to the project connection manager ServerName property. When I right-click on the SSIS project node in SSMS 2012, launching the Configure dialog box, I can locate the Connection Manager, and highlight it to see its properties, but ServerName is not visible in the Properties list. Usually, the ServerName property is listed under the RetainSameConnection property. It's visible on other Project Connection Managers in the same project. Why would this property be hidden, just for one Connection Manager?