First you have to hit Reply, which will lets you compose a message, but instead of doing that click the button with a down arrow next to the 'To:' field. That will show a drop down menu with an option to edit the subject line. Click Edit subject.
The email subject line is now visible and editable!
I don't know why Gmail doesn't always show the subject line when composing replies, but at least following the steps above you can change it if necessary.