The numerous pores and cavities present in adhesive underfills increase the susceptibility of microelectronic packages to Type II cracking. In this work, we focus on the effects of softening-rehardening and pressure-sensitivity on adhesive failure. An axisymmetric unit-cell study is first performed to ascertain the failure mechanisms in a softening-rehardening polymer. Results show that shear banding is the dominant failure mechanism under low stress triaxiality, while internal necking is the likely failure mode for highly constrained pressure-sensitive adhesives. With this in mind, a population of discrete voids is introduced ahead of a crack in an adhesive sandwiched between elastic substrates. We show that strain softening tends to lower the stress-carrying capacity of the adhesive, while strain rehardening suppresses both the intensity and spatial extent of damage. An increase in the rate of rehardening also reduces the oblacity of the voids. For adhesives with high pressure-sensitivity, rapid voiding occurs throughout the adhesive at low loads, leading to formation of extended damage zones.