The source of the problem is the build.properties file and changes to properties in the file between Sencha Cmd v3.1.2.342 and v4.0.2.67. The file is located in the project root:
.sencha/app/build.properties
By clearing out all of the custom properties in build.properties we were able to run the refresh and build commands successfully:
$ sencha app refresh
$ sencha app build
The source of the problem was our project was generated by Sencha Cmd v3.1.2.342. When we upgraded to Sencha Cmd v4.0.2.67 and the project went through the upgrade process. The format of the file and the properties changed. The legacy properties used by Sencha Cmd v3.1.2.342, and some paths, no longer existed with Sencha Cmd v4.0.2.67. The merge process during the upgrade does its best to keep your legacy properties; even if they break things. Breaking the build.
I would recommend creating a sample project with Sencha Cmd v4.0.2.67, and perform a diff of the sample project build.properties file against the project where the build is broken. We had about 70 lines of custom properties for output directories, SASS and CSS paths that were no longer valid.