CRM_2016-03-17_13-29-30.png
I am appending bootstrap chosen drop-down on button click, the javascript is not triggering that why it is showing simple multiple select.

    $(document).on('click', '#more_provisions_button',  function () { 
    console.log('Incre : '+i);
    $("#provision_div").append("<p class='par'><div class='form-group' style='clear:both'><div class='col-sm-6 mr-bottom'><select name='provision_month[]' id='day' class='chosen-select input-md' style='width:500px;'><option value='January'>January</option><option value='February'>February</option><option value='March'>March</option><option value='April'>April</option><option value='May'>May</option><option value='June'>June</option><option value='July'>July</option><option value='August'>August</option><option value='September'>September</option><option value='October'>October</option><option value='November'>November</option><option value='December'>December</option></select></div><div class='col-sm-4 mr-bottom'><select required name='provision_day[]' multiple='' id='ass_letter_date' class='chosen-select input-md' style='width:500px;'><option value='1'>1</option><option value='2'>2</option><option value='3'>3</option><option value='4'>4</option><option value='5'>5</option><option value='6'>6</option><option value='7'>7</option><option value='8'>8</option><option value='9'>9</option><option value='10'>10</option><option value='11'>11</option><option value='12'>12</option><option value='13'>13</option><option value='14'>14</option><option value='15'>15</option><option value='16'>16</option><option value='17'>17</option><option value='18'>18</option><option value='19'>19</option><option value='20'>20</option><option value='21'>21</option><option value='22'>22</option><option value='23'>23</option><option value='24'>24</option><option value='25'>25</option><option value='26'>26</option><option value='27'>27</option><option value='28'>28</option><option value='29'>29</option><option value='30'>30</option><option value='31'>31</option></select></div></div></p>");
    i++;
    return false;
     });

Which bootstrap multiple select plugin are you using? Doens't look like anyone I know.

Any how, your select is missing multiple='multiple'

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