My solution with extra credit code done. Here it is using a do/while loop, what do you think?

// The Object
var students = [
    {name: 'Karen', 
     tracks: 'Data Bases, SQL, MYSQL', 
     achievements: 120, 
     points: 8
    },
    {name: 'Roberto', 
     tracks: 'Marketing, MBA', 
     achievements:100, 
     points: 10
    },
    {name: 'Diego', 
     tracks:'PHP, SQL, .NET, JS', 
     achievements:120, 
     points:11
    },
    {name: 'Ignacio', 
     tracks:'IOS, ANDROID', 
     achievements:130, 
     points:8
    },
    {name: 'Giovanni', 
     tracks:'HTML5, CSS3, BOOTSTRAP, JS, JQ', 
     achievements:125, 
     points:9
    },
  {name: 'Ignacio', 
     tracks:'IOS, .NET', 
     achievements:100, 
     points:7
    },
  {name: 'Roberto', 
     tracks: 'Project Manager, Art Direction', 
     achievements:90, 
     points: 10
    }
];

//var definition
var message = '';
var student;
var search;
// this array holds the students found
var studentsArray = [];

//print function
function print(message) {
    var outputDiv = document.getElementById('output');
    outputDiv.innerHTML = message;
}

//Information for Print Function
function studentList(studentsArray) {
  var information = ''; 
  for (l = 0; l < studentsArray.length; l +=1){
    information += '<h2>Student: ' + studentsArray[l].name + '</h2>';
    information += '<p>Tracks: ' + studentsArray[l].tracks + '</p>';
    information += '<p>Points: ' + studentsArray[l].points + '</p>';
    information += '<p>Achievements: ' + studentsArray[l].achivements + '</p>';
  }
  return information;
};

//The Loop
do {
  // Update Students Arrays, empty the array for a new search.  
  studentsArray = [];   
  // ask for a student name
  search = prompt('Search Student Record: type a name, for example [Dave], to end type [quit]');
  // If result is null break else not found in record 
  if (search === null) {
    break;
  } else {
     message ='<h2>The Student Name: ' + search + ' is not part of our Students Records</h2>';
     print(message);
  }
  //loop through the students Array of objects and compare / search for a name
  for (var i = 0; i < students.length; i += 1) {
    student = students[i];
    if (student.name.toLowerCase() === search.toLowerCase()){
      // push every student and matching student into studentsArray
      studentsArray.push(student);   
      //Print the result in the document
      message = studentList(studentsArray);    
      print(message);
      }
  }
} while (search.toLowerCase() != 'quit')
// Go!!!