Adding and using html with jquery works only sometimes

It's not apparent in the code why .entityselector() should throw on some occasions. The most likely reason is that you are trying to invoke the plugin before it is loaded.

In an attempt to fix the issue, you might try initialising all the inputs in one hit instead of individually in the loop.

Also, the code would be made more readable by attaching a fairly simple fragment to the DOM, then immediately adding links and attaching event handlers with jQuery.

Here it is the way I would write it (with a bunch of tidying up) :

function addlinks(qid, prop) {

    // compose and intert fieldset.
    var $fieldset = $("<fieldset><legend>Quick Presets (" + prop.name + ")</legend></fieldset>")
        .insertAfter($('.wikibase-statementgrouplistview').first());

    // loop through prop.defaults
    prop.defaults.forEach(function(dflt) {
        // compose and append a basic fragment ...
        var $fragment = $("<p class='addstatement'>Add " + dflt.pname + ":<span class=\"links\"></span>"
            + "<span class=\"quickpresetsinput\"><input />&nbsp;<a href=\"#\">✔</a></span></p>")
            .appendTo($fieldset);

        // ... then allow jQuery to augment the appended fragment :
        // i) conditionally addClass('disabled')
        if($('#P' + dflt.pid).find(".wikibase-snakview-value a").length !== 0) {
            $fragment.addClass('disabled');
        }

        // ii) loop through dflt.values and add links.
        dflt.values.forEach(function(val) {
            $("<span>&nbsp;<a href=\"#\"></a>&nbsp;∙</span>")
            .appendTo($fragment.find('span.links'))
            .find('a')
            .text(val.name)
            .on('click', function(e) {
                e.preventDefault();
                additemstatement(qid, dflt.pid, dflt.pname, val.qid, val.name);
            });
        });

        // iii) attach click handlers to the quickpresets inputs
        $fragment.find('.quickpresetsinput').find('a').on('click', function(e) {
            e.preventDefault();
            var selection = $(this).prev('input').data('entityselector').selectedEntity();
            additemstatement(qid, dflt.pid, dflt.pname, selection.id.substring(1), selection.label);
        });
    });

    // invoke .entityselector() on all the quickpresets inputs in one hit
    $('.quickpresetsinput input').entityselector({
        'url': 'https://www.wikidata.org/w/api.php',
        'language': mw.config.get('wgUserLanguage')
    });
}

untested except for syntax

That's certainly tidier though without a proper understanding of the original issue, .entityselector() may still throw.