The development of high-field accelerator magnets capable of providing 16-T dipolar fields is an indispensable technological breakthrough needed for the 100-TeV energy frontier targeted by the Future Circular Collider. As these magnets will be based on Nb3Sn Rutherford cables, the degradation of the conductor performance due to the large electromagnetic stresses becomes a parameter with a profound impact on the magnet design. In this work, we investigated the stress dependence and the irreversible reduction of the critical current under compressive transverse load in high-performance powder-in-tube Nb3Sn wires. Tests were performed in magnetic fields ranging between 16 and 19 T on wires that were resin impregnated similarly to the wires in the Rutherford cables of accelerator magnets. The scope was to predict the degradation of the cable under stress from a single-wire experiment. Interestingly, the irreversible stress limit, σirr, defined as the stress level corresponding to a permanent reduction of the critical current by 5% with respect to its initial value, was found to depend on the applied magnetic field. This observation allowed us to shed light on the mechanism dominating the irreversible reduction of the wire performance and to compare and reconcile our results with the irreversible limits measured on Rutherford cables, typically tested at fields below 12 T.