If my radio hardware does not change, do I need to update my certification when I add new firmware or bands?

Yes, potentially. Certification is tied to how the transmitter operates, not just the physical hardware. Adding new frequency bands, enabling higher duty cycles, changing modulation behavior, increasing output power, or activating new operating modes can materially change the compliance basis. Even changes that appear software-only can trigger regulatory impact if they affect emissions, spectrum use, or RF exposure. FCC and ISED both expect manufacturers to evaluate whether changes fall within the scope of the existing grant or require a permissive change or new filing. Assuming firmware changes are exempt is a fast way to end up with an invalid certification.