Can my rank ever change?

Yes, if the recruitment is continuous/open until filled, new names will be added to the list each time the exams are administered. If another applicant scores higher than you, your rank will be lowered. It is also possible for you to advance higher on the eligible list as others are hired or removed for other reasons such as finding other jobs. In addition, your rank may change from one recruitment to another even if the same exam is used.