Actually, it is connected to the main supply. I have one and when I disconnect the main battery, I still have 12 volts in the system. I must disconnect the auxillary battery as well in order to get the car's electricity system dead. The battery supports the petrol heater and the phone, as DrSakke says.
In my boat, I have a twin battery set-up for the normal use of electricity (lamps, navigation, refrigirator, radio, wind instruments, eco sounding etc)plus one start battery for the engine. If one of the two batteries in the "consumer cirquite" is bad, it will consume whatever the good battery can deliver. The result is very low capacity all the time even if the alternator works its socks off.
I have had this experience more than once.
I suggest that you check the capacity of your auxilary battery at a shop where they know what they are doing.
The other option is that your alternator is gone. It may produce just enough electricity when driving but cannot add anything to the "buffer". I know you said you have a new alternator, but if the batteries were very low when you engaged the new alternator, it may have been busted. I have just changed my alternator and I was informed (warned) that bad battries may kill my new alternator. So far, I'm OK.