I have tested the behavior on a test Sitefinity 3.7 project and it seems that there is an issue sorting the documents by Publication date. You may refer to the following forum thread
where the same issue has been discussed.
Sorting by publication date is working properly in the latest Sitefinity version (Sitefinity 7.1) for the DownloadList widget. What we could suggest is to perform a migration to some of the latest Sitefinity versions in order to take advantage of this functionality as well as all the features
and fixes which have been included.
More information about the migration process could be found on the following article
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items