Next Ajax call doesn’t work

As the “Next”, “Prev” links are the part of AJAX responded content, you need to use either 'live' or 'on' based upon the jQuery version you are using.

jQuery(document).ready(function($) {
    var cadenaNext="";
    var cadenaPrev='';
    $('#ajax-form-next').live("submit", function(e) { 
                e.preventDefault();
                jQuery.post(MyAjax.url, {action : 'next_posts' ,cadenaNext : $('#nextPosts').val(), cadenaPrev : $('#actualPosts').val() }, function(response) {
                $('#posts_container').hide(1000);
                setTimeout(function() {$('#posts_container').html(response).show(1000);}, 1000);
            });
    });

    $('#ajax-form-prev').live("submit", function(e) { 
                e.preventDefault();
                jQuery.post(MyAjax.url, {action : 'next_posts' ,cadenaNext : $('#prevPosts').val(), cadenaPrev : $('#actualPosts').val() }, function(response) {
                $('#posts_container').hide(1000);
                setTimeout(function() {$('#posts_container').html(response).show(1000);}, 1000);
            });
    });

});