This paper aims to quantify how the lowest halo mass that can be detected with galaxy-galaxy strong gravitational lensing depends on the quality of the observations and the characteristics of the observed lens systems. Using simulated data, we measure the lowest detectable NFW mass at each location of the lens plane, in the form of detailed sensitivity maps. In summary, we find that: (i) the lowest detectable mass M low decreases linearly as the signal-to-noise ratio (SNR) increases and the sensitive area is larger when we decrease the noise; (ii) a moderate increase in angular resolution (0.07 '' versus 0.09 '') and pixel scale (0.01 '' versus 0.04 '') improves the sensitivity by on average 0.25 dex in halo mass, with more significant improvement around the most sensitive regions; (iii) the sensitivity to low-mass objects is largest for bright and complex lensed galaxies located inside the caustic curves and lensed into larger Einstein rings (i.e r(E) >= 1.0 ''). We find that for the sensitive mock images considered in this work, the minimum mass that we can detect at the redshift of the lens lies between 1.5 x10(8) and 3 x10(9) M-circle dot. We derive analytic relations between M-low, the SNR and resolution and discuss the impact of the lensing configuration and source structure. Our results start to fill the gap between approximate predictions and real data and demonstrate the challenging nature of calculating precise forecasts for gravitational imaging. In light of our findings, we discuss possible strategies for designing strong lensing surveys and the prospects for HST, Keck, ALMA, Euclid and other future observations.