Database field is correct, that needs changing. You need phpMyAdmin to access your database, find the table phpbb_posts_text, the field post_subject, and change varchar(60) to varchar(255)
Find the table phpbb_topics, field topic_title, and make it exactly the same - the topic title is a copy of the post title of the first post.
You can now just use the template to limit the length again if you like:
find something similar to this in posting_body.tpl:
<input type="text" class="post" name="subject" size="45" maxlength="60"
and change maxlength to another number