Yes, you can hide tasks where all of the slots in the task happened in the past.  Slots that happened int he past will still be displayed in the same task with other current slots, but they will not have a Volunteer button.
To make sure this works
Under the Settings tab | Display sub-tab check the option “Hide old tasks.” Then press Save.
You must put in the correct dates into the field designated for DATEs and NOT just in the text fields of headers.  Check the Task Date Option for each task.  If it is “Task is on one day” make sure the correct Task Date is provided.  If it is “Dates are in Column or Row Headers” make sure the correct date is put into the Date field of the relevant Column or Row headers.  If it is “Dates are in each Slot Position” make sure the correct date is put into the Date field of each slot.
To learn more about how dates work in ivolunteer.com, take a look at this video.