Are you referring to the WAN IP of the MX? If it's a static IP, then by definition it shouldn't change. How is the IP allocated? Some providers for example use DHCP, but assign that circuit the same public IP address, regardless of the MAC at the other end. Others you will use PPPoE, others still will have you statically assign yourself as a /31 or /30. You are probably best off check with whoever supplies the underlying circuit.