There are a couple of options.
1) Whether or not old answers are shown is controlled by the "show saved answers" or "show old answers" display option. The default is to show old answers, but its possible that that is different on your server for some reason. If you are using 2.10, you might check to see if the "show saved answers" option is enabled by going to user settings. Otherwise that setting is under "Display Options". You can also check the Permissions area of Course Configuration to see if the "Can Show Old Answers" permission is set to student.
2) As a fall back, students can see previous answers, along with their comments, by using the Show Past Answers button, assuming that they have permission to do so.
In either case this is an issue of how your server is set up to deal with old answers, and not an essay question specific problem.