If you see the battery discharge light, then (single battery) it has a min of 30 mins remaining.
As I understand it, the battery bus and dc standby bus will remain connected to the main system with the STANDBY POWER switch in AUTO and TR3 functioning, so those buses will remain powered. However, the hot battery buses will not be powered once the battery is flat, APU and engine fire extinguishing will not be available.
For that reason I think popping in to visit the nearest suitable (in time) a rational and safe choice.