This was resolved in Raiser's Edge 7.96 patch 2, released in January-February 2017 and applied to databases in Blackbaud Hosting Services. If your database is installed locally, download and install the latest version and patch, if applicable.
1. Click on the column you want to sort by on the Participants tab
2. Save and close the event
3. Reopen the event - the Particpants tab is sorted by desired column