With a diode module between the battery and the DC bus you have an automatic switching that inserts the main battery in the bus WHEN THE BUS VOLTAGE IS BELOW BATTERY MINUS DIODE VOLTAGE DROP. To keep the 32 V battery "disconnected" the bus voltage must be operating above 33,5 V or so.
Interesting point. Is is just a diode? Lithium cells can be damaged by over discharging. I would hope there was something that protected the battery from feeding the bus via the diode if the bus voltage was too low for some reason. eg I would hope it's not a simple diode but a diode and an electronic switch with under voltage detection.
You have to be quite careful about recharging a lithium battery that has been allowed to go too flat.