.click() will only add event handlers to the current DOM.
If you want jQuery events to also apply to any HTML that is subsequently loaded via AJAX, you need to use the .on() event handler rather than .click():
$(document).ready(function() {
$('body').on('click', '.content', function() {
$(this).parent().removeClass("highlightedbroadcast");
var broadcastid = ($(this).parent().attr("id"));
});
});
Either that, or you need to add the click events to HTML that is loaded via AJAX after every AJAX call.