Once a participant takes a hardship withdrawal, should his salary deferral start back up automatically after 6 months, or should the participant be contacted to complete another election form? Is there any problem/issue with the administrator starting the deferral back up automatically?

Does your plan document address this issue?

If the document doesn't say anything, then unless the participant has changed his election, deferrals should re-start when they are no longer prohibited; i.e. you are simply following the participant's election.