Blusafe Origin Smart is battery operated and works via Bluetooth; therefore you are never locked out. You will still be able to use your fingerprint, key-card or App if there is a power cut.
The only functionality that will be affected is when using the Wi-Fi bridge as it requires an internet connection. This only affects unlocking the door remotely however, all other functions will not be affected.
Blusafe Breeze is battery operated and has no connection to the internet, therefore the lock will work regardless. If the batteries die, it still has a manual backup key.
Blusafe Mirage is powered by an internal, rechargeable battery, therefore the lock will work providing it has charge. If the battery dies, it can be powered via a Micro USB cable.