Widget Update problems using a for loop

Please replace below line:

echo "<input class="widefat" type="text" value="{$instSpecLine}" name="{$instSpecLine}" id='{$instSpecLine}' placeholder="Spalte {$j}" >";

With Below code:

echo "<input class="widefat" type="text" value="{$instSpecLine}" name="".$this->get_field_name("spec_line_{$i}_{$j}")."" id='{$instSpecLine}' placeholder="Spalte {$j}" >";

Hope this will help you