Hi ribo
By default, this dropdown will show up only when the slideshow position is used on current page.
For example, there is a module assigned to 'slideshow' position on homepage so this dropdown appears on homepage only, not other pages.
If you want to show it on all pages, you can edit this file:
/templates/ja_autoshop/tpls/blocks/mainnav.php
Look for this line of code - at approx line 32:
<div class="t3-navbar-category <?php $this->_c('navbar-category') ?> <?php if (!$this->countModules('slideshow')) echo "category-dropdown"; ?>">
change it to:
<div class="t3-navbar-category <?php $this->_c('navbar-category') ?> ">