Try this solution for keep selected value in dropdown:
<form action="<?php echo get_page_link(); ?>" method="post">
<select name="<?php echo $field_key['key']; ?>" onchange="javascript:
submit()">
<option value="">All Category</option>
<?php
foreach( $field['choices'] as $key => $value ){
if($post_key==$key){ ?>
<option value="<?php echo $key; ?>" selected><?php echo $value; ?></option>
<?php
}else{?>
<option value="<?php echo $key; ?>"><?php echo $value; ?></option>
<?php }
}?>
</select>
</form>