@andrewg the app is prompting for the folder with a message of the form "Looks like the TeX file you are importing includes or imports other TeX files. Please grant access to the folder that contains all the included or imported TeX files by clicking 'Choose' below."
The prompt is not on the most visible spot possible and we'd love to make this whole process go away, but it is unfortunately made necessary because of restrictions set to us by the OSX sandbox (which does give the app a lot of good security related properties). However, there is actually no limit of 3 attempts, it sounds more like you have eventually got through the confusing screen successfully and the app now has access to the files it needs, but importing fails downstream of that.
Would you mind sending us the LaTeX project that fails to import via email@example.com, please? We have a good history of being able to resolve document specific import and export issues and will do our best to make the project import. Are all the files under a single root directory, or scattered in more creative ways? The latter scenario is something we do not currently handle and it is made hard by the sandbox (you need to provide access for the app to the directory that is the common ancestor between all the TeX files being referenced by the main file you try to import).
CEO & Co-founder of Manuscripts.app Ltd