1200w dc-dc boost converter low voltage protection not working
Yes, this boost converter is designed to continue passing power, but you could easily add an undervoltage protection circuit that would completely disconnect the power source.
It could be as simple as a 12 volt DC relay in series with a 12 volt Zener diode, and a startup switch to bypass the diode, connected to the 24 VDC output. When starting, you'd need to hold the start switch, applying 12 VDC directly to the relay. Once 24 V is available, 12 volts would be dropped across the Zener, and the relay would have its rated 12 V. If the power falls back, the relay would drop out.
Another way to disconnect the battery would be to connect a relay from the battery positive to the boost output. While there's a 12 volt difference (i.e., the converter is boosting), the relay would be held closed. Again, some startup mechanism is needed.
You could also design or buy a circuit that auto-starts, without the switch, though requiring manual intervention could be an advantage for safety and to reduce the chance of battery discharge.