Assuming there was a significant schedule change (60+ Minutes), the connection is no longer feasible (below MCT), or a change in operating carrier, then in my opinion, you shouldn't have any issues making the change with no fee (even with the certificate).

It's worth a call if you have a better flight in mind, just call and explain there was a schedule change and you have an alternate flight in mind. When it comes to schedule changes agents have a lot of flexibility.