In this paper, we study how the power dissipated into a lossy medium excited by a nearby antenna is affected by drifts in the electrical parameters of the lossy medium. The statistical distribution of the sensitivity of the dissipated power is determined by means of a spectral analysis of the transmission of electromagnetic energy from air into the lossy half-space. A clear link is drawn between the reactive content of the field excited by the source and the dispersiveness of the sensitivity. The case of a stratified structure is also addressed, by defining a modification factor representing the alteration of the transmissivity and of its sensitivity when a buffer layer is introduced. All of the results provided point out that, in general, the sensitivity of the total amount of power dissipated into the half-space cannot be predicted independently from a precise knowledge of the source characteristics, unless under a paraxial propagation approximation or in a far-field configuration.