If I use it as it is, without modifying or overwriting it, it works perfectly fine.
But if I change anything, or simply overwrite it by saving it (even if I didn't change anything) the form doesn't work properly anymore when I open the dynamic PDF form.
BUT, if I modify it/save it and go in the 'Preview PDF' tab of LiveCycle, the form works perfectly fine and I'm able to use the searchable drop-down list.
To summarize, it seems like the dynamic form doesn't work properly when saved and opened with a reader (I'm using Adobe Reader), but it works fine in the PDF Preview from LiveCycle Designer.
Looking forward to your answers!