The pressure-based, current-driven impedance control technique known as "Electroacoustic Absorption" has offered new horizons for room modal equalization at low frequencies, steerable anomalous reflection, acoustic transmission attenuation and non-reciprocal wave propagation. Nevertheless, its level of performance is strongly limited by stability constraints. A primary source of instability is the loss of acoustical passivity due to time delay in the digital implementation of the controller. In this paper, the effect of time delay on the Electroacoustic Absorber stability is verified by correlating, both numerically and experimentally, the loss of acoustical passivity at high frequencies to the upsurge of instability in a one-dimensional closed cavity. Then, we show the effect of placing a porous layer in front of the Electroacoustic Absorber, allowing to counteract for the loss of acoustical passivity and enlarge the passivity margin. Finally, we provide an integral constraint on the absorption spectrum valid for the pressure-based, current-driven architecture of the Electroacoustic Absorber. It generalizes the integral constraint for purely passive absorbers to electro-active impedance controlled loudspeakers, and demonstrates the close interdependence between absorption bandwidth, passivity, and electrical source supply by a straightforward analytical expression.