My solution

var message;
var student;
var search;

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

function gerStudentReport ( student ) {
  var report = '<h2>Student: ' + student.name + '</h2>';
  report += '<p>Track: ' + student.track + '</p>';
  report += '<p>Points: ' + student.points + '</p>';
  report += '<p>Achievements: ' + student.achievements + '</p>';
  return report;
}

while (true) {
  search = prompt('Search student records: type a name [Jody] (or type "quit" to end)');
  message = '';
  var existence = false;

  if (search === null || search.toLowerCase() === 'quit') {
    break;
  }

  for (var i = 0; i < students.length; i += 1) {
    student = students[i];
    if (student.name === search) {
      message += gerStudentReport( student );
      print (message);
      existence = true;
    }  
  }

  if ( !existence ) {
    alert('There is no such student in database.');
  }
}