WordPress select dropdown list in widget

See my comment above…you’re using get_field_id() on the name-attribute, where it should be get_field_name().

get_field_id() returns 'widget-'.$this->id_base.'-'.$this->number.'-'.$field_name,
whereas
get_field_name() returns 'widget-'.$this->id_base.'[' . $this->number . '][' . $field_name.']'