Update post meta without deleting the old entries

Please try to replace:

update_post_meta( $post_id, 'figure_sugsubject_repeatable_fields', $new );

with:

add_post_meta( $post_id, 'figure_sugsubject_repeatable_fields', $new );

to add more values related to the figure_sugsubject_repeatable_fields meta key.

You should also consider using filter_input() instead of $_POST.

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