Sometimes, a rather high stress drop characterizes earthquakes induced by underground fluid injections or productions. In addition, long-term fluid operations in the underground can influence a seismogenic reaction of the rock per unit volume of the fluid involved. The seismogenic index is a quantitative characteristic of such a reaction. We derive a relationship between the seismogenic index and stress drop. This relationship shows that the seismogenic index increases with the average stress drop of induced seismicity. Further, we formulate a simple and rather general phenomenological model of stress drop of induced earthquakes. This model shows that both a decrease of fault cohesion during the earthquake rupture process and an enhanced level of effective stresses could lead to high stress drop. Using these two formulations, we propose the following mechanism of increasing induced seismicity rates observed, e.g., by long-term gas production at Groningen. Pore pressure depletion can lead to a systematic increase of the average stress drop (and thus, of magnitudes) due to gradually destabilizing cohesive faults and due to a general increase of effective stresses. Consequently, elevated average stress drop increases seismogenic index. This can lead to seismic risk increasing with the operation time of an underground reservoir.