Keep Bootstrap Dropdown Open When Clicked Inside

You can use the following JavaScript to manually open and close the dropdown menu:

$(function() {

  $('.dropdown-toggle').on('click', function(event) {
    $('.dropdown-menu').slideToggle();
    event.stopPropagation();
  });

  $('.dropdown-menu').on('click', function(event) {
    event.stopPropagation();
  });

  $(window).on('click', function() {
    $('.dropdown-menu').slideUp();
  });

});

Demo in StackSnippets

$(function() {

  $('.dropdown-toggle').on('click', function(event) {
    $('.dropdown-menu').slideToggle();
    event.stopPropagation();
  });

  $('.dropdown-menu').on('click', function(event) {
    event.stopPropagation();
  });

  $(window).on('click', function() {
    $('.dropdown-menu').slideUp();
  });

});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" />

<div id="navbar">
  <nav class="navbar navbar-default navbar-static-top" role="navigation">
    <ul class="nav navbar-nav">
      <li class="dropdown">
        <a href="#" class="dropdown-toggle" data-toggle="dropdown">MENU</a>
        <div class="dropdown-menu">
          <p>Hello</p>
          <input type="text">
        </div>
      </li>
    </ul>
  </nav>
</div>


From the question Avoid dropdown menu close on click inside, you can simply stop propagation from inside the dropdown like this:

$(document).on('click', '.allow-focus .dropdown-menu', function (e) {
  e.stopPropagation();
});

Demo in Stack Snipets

$(document).on('click', '.allow-focus .dropdown-menu', function (e) {
  e.stopPropagation();
});
<link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet"/>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.4/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/js/bootstrap.js"></script>


<div class="dropdown allow-focus">
  <button id="dropdownLabel" type="button" class="btn btn-default"
          data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
    Dropdown trigger
    <span class="caret"></span>
  </button>
  <div class="dropdown-menu panel" aria-labelledby="dropdownLabel">
    <div class="col-xs-12">
      What's Your Name?
      <input type="text" placeholder="Name" class="form-control" />
    </div>
  </div>
</div>

NOTE: To solve the opposite problem (of keeping open until clicked), you can refer to:

Keep Bootstrap Dropdown Open When Clicked Off