The answer depends on your make and model..
In the old days the isolator relay was operated by the ignition switch for the most part, It connected the two systems only when the engine was running, This system is lower in cost than what I will describe next so .... Of course back then when the engine was OFF it was OFF, I mean there was no engine control computer that needed full time power, The Radio really turned OFF, about the only thing that might draw power.. Was a clock.
Today There are many "Vehicle" systems that still draw power. I listed 3 of them above but here may even be more.. So a vehicle just sitting eats it's battery.
So they developed the Bi-Directional Isolator.. (We refer ot it as a BIRD here, Bi-directional Isolator Relay Delay) This device measures voltage both sides of the realay and if it sees a high enough voltage (I do not know the trip point but let's say 13 volts) it closes so the house can charge the chassis, or the other way around after a delay of say 30 seconds.
So the two answers, depending on the make and model are:
1: We did not install a BIRD
2: BIRD defective.
NOW TO FIX:
Two ways
1: Upgrade isolator and control to BIRD system (Expensive)
2: Trick-L-Start,, This is a monodirecitonal isolator just like the one you have now.... but in the other direction, Simple 3 wire hookup (Both of the big wires on the isolator relay plus ground) fully automatic operation.