We examine the mechanical properties of graphene devices stretched on flexible elastomer substrates. Using atomic force microscopy, transport measurements, and mechanics simulations, we show that micro-rips form in the graphene during the initial application of tensile strain; however subsequent applications of the same tensile strain elastically open and close the existing rips. Correspondingly, while the initial tensile strain degrades the devices' transport properties, subsequent strain-relaxation cycles affect transport only moderately, and in a largely reversible fashion, yielding robust electrical transport even after partial mechanical failure.