If any issues occur during the file or attachment download, the Mass File Download app won't allow you to resume. You'll need to search again and initiate a new download once you're back on your computer.
PS: View Mass File Download, Salesforce file download app on Salesforce AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000EcsAOUAZ