Reddit automatically marks all messages as read when you open the messages page, however there's a checkbox in preferences that you can disable if you don't like this behavior which, when disabled, forces you to click on messages to mark them as read.

There is a Checkbox in preferences where it will make all reddit links open in a new window if that helps.

Yeah, as soon as you open your inbox, it marks all the messages in there as read. You can click on "post replies" from your empty inbox to see them again, though. Or just remember to open links in a new window.