Subsurface fluid flow is ubiquitous in nature, and understanding the interaction of multiple fluids as they flow within a porous medium is central to many geological, environmental, and industrial processes. It is assumed that the flow pathways of each phase are invariant when modeling subsurface flow using Darcy's law extended to multiphase flow, a condition that is assumed to be valid during steady-state flow. However, it has been observed that intermittent flow pathways exist at steady state even at the low capillary numbers typically encountered in the subsurface. Little is known about the pore structure controls or the impact of intermittency on continuum scale flow properties. Here we investigate the impact of intermittent pathways on the connectivity of the fluids for a carbonate rock. Using laboratory-based micro computed tomography imaging we observe that intermittent pathway flow occurs in intermediate-sized pores due to the competition between both flowing fluids. This competition moves to smaller pores when the flow rate of the nonwetting phase increases. Intermittency occurs in poorly connected pores or in regions where the nonwetting phase itself is poorly connected. Intermittent pathways lead to the interrupted transport of the fluids; this means they are important in determining continuum scale flow properties, such as relative permeability. The impact of intermittency on flow properties is significant because it occurs at key locations, whereby the nonwetting phase is otherwise disconnected.