When called for the fan is supposed to run for 1 hour. Its not factory its something I have made for an experiment I'm working on. Anyway... I wonder what the vehicle manufacturers use and what voltage they are using as a set point to trigger a low battery alarm be sent to the cars information center on these new fancy cars. My in laws car sent an alert last year when we were sitting at the drive in movie theater with the radio and interior lights on for too long. That is what got me thinking about creating this circuit in the first place.I follow the reasoning but with a battery that is too weak to run a 5 - 6 amp load for an hour its standing voltage when charged will be too low to begin with making the disconnect false trip all the time.
A new battery when fully charged will stay around 12.5 - 12.9 volts for a long time and even if ran down to around 10% charge will still hold 12+ volts while having enough amperage generating capacity to start the engine.
Whereas with a old worn out battery it may not even hold 12 volts at full charge and will drop off fast from there so even if you cut it off at 11.5 volts it may very well not have enough reserve capacity to produce the amperage needed to start the engine without dropping well below the cut off circuit tripping point if it can start it at all.
Battery protection device work well on new good condition batteries but on old worn out ones they are pointless and just make a nuisance of themselves.
That and very few vehicles have radios that hold their programed settings so every time the battery cut off trips you have to go in and reset everything plus possibly put up with your vehicle's engine computers having to reset and relearn their settings as well.
Personally if it was me I would be looking at why the fan runs after the ignition is off and fixing that design issue. I don't know of any vehicle that does that on purpose.