Not too long ago the developers of the LayerSlider plugin made some significant changes. (For everyone in general who may read this topic) The location where a custom skin for the slider goes is one, and the other is that the export/import is now done in a .json file format is the second big change.
As for your question…this is one you will want to contact them about if your importing of the exported .json file is not importing. Also, if the zip file it generated when exporting is not able to open in winrar (which I use and prefer) or winzip, it could be a corrupt zip file….might want to inform them of this as well. I just downloaded an export to my desktop from one of my demo sites and using winrar, I did get the file unzipped. Again, it could be a corrupt export file; perhaps try once again.