If you are having issues running the Papers 3 importer from the desktop app there are a few things you can do. First, refer to this troubleshooting guide to make sure your computer stays on, your computer stays connected to the internet, and you have a nice coffee as the process can take some time.
If you have followed this guide and keep running into trouble there is an additional step you can take. First backup your Papers 3 Library by zipping up the folder and storing it somewhere else on your hard drive. Once complete open Papers 3. Go to Help -> Troubleshooting -> Repair Library.
This operation will delete any faulty references or any PDF's that it can't open. Since this operation can delete some files make sure you backup your library before doing this operation. The amount of time for a repair can vary but for a library that is under 20 GB's it should take less than 15 mins. Once the repair is done you can try importing your library again. If you have issues or problems please don't hesitate to reach out to support@papersapp.com