The retention of electrical performance under the combined conditions of mechanical strain and an electrical current is essential for flexible electronics. Here, we report that even below the critical current density required for electromigration, the electrical current can significantly deteriorate the electromechanical performance of metal film/polymer substrate systems. This leads to a loss of stretchability, and this effect becomes more severe with increasing strain as well as increasing current. The local increase of electrical resistance in the metal film caused by damage, such as localized deformations, cracks, etc., locally raises the temperature of the test sample via Joule heating. This weakens the deformation resistance of the polymer substrate, accelerating the necking instability, and consequently leading to a rapid loss of electrical conductivity with strain. To minimize such a current-induced deterioration of the polymer-supported metal films, we develop and demonstrate the feasibility of two methods that enhance the deformation resistance of the polymer substrate at elevated temperatures: increasing the thickness of the polymer substrate, and utilizing a polymer substrate with a high glass transition temperature.