Just replace this:

function add_tags_textinput() {
	global $postdata;
	$tags = get_post_meta($postdata->ID, 'tags', true);

with this:

function add_tags_textinput() {
	global $post_ID;
	$tags = get_post_meta($post_ID, 'tags', true);

The problem is that it will show existing tags, or let you add a new tag, but it will lose tags when you edit a post. It’s not able to retrieve the tags to fill in the form field, apparently because $postdata isn’t returning the ID it expects.

I’ve submitted the fix to wp-plugins.org, so if the author is keeping track of tickets there, the fix should show up in the next version of the plugin.

Update Jan. 3: The plugin author has released version 0.5 with a slightly different fix (plus a few other improvements), and it’s now compatible with WordPress 2.0.