Why is a linear passive circuit stable, i.e. why does its impulse response approach zero over time?
In a circuit that is composed of only Ls, Cs and Rs ...

An input impulse will store energy in the Ls and Cs. The stored energy will be dissipated in the Rs, and will tend to zero over time. 

Conversely, if there are no Rs, no means of dissipation, then the energy will remain stored, and the impulse response will last indefinitely.