(How) Can we avoid missing new physics at the LHC?

Despite of its great success in describing the world of elementary particles, the Standard Model (SM) fails to explain certain phenomena: It does not include gravity, it accommodates neither neutrino masses nor dark matter, and it predicts a miniscule baryon asymmetry. These shortcomings indicate that the SM is not a complete theory of nature - suggesting the necessity of its extension and the existence of new physics, beyond the SM (BSM).
The many searches for BSM scenarios, particularly in the general-purpose experiments, ATLAS and CMS, have not shown to date deviations from the (SM) predictions. Could we be missing a discovery? In this talk, I will discuss some of the actions we take to minimize this risk.