The influence of fluid properties on the critical pressure of permeation of an oil micro-droplet into a slotted pore is studied numerically by solving the Navier-Stokes equations. We consider a long slotted pore, which is partially blocked by the oil droplet but allows a finite permeate flux. An analytical estimate of the critical permeation pressure is obtained from a force balance model that involves the drag force from the flow around the droplet and surface tension forces as well as the pressure variation inside the pore. It was found that numerical results for the critical pressure as a function of the oil-to-water viscosity ratio, surface tension coefficient, contact angle, and droplet radius agree well with theoretical predictions. Our results show that the critical permeation pressure depends linearly on the surface tension coefficient, while the critical pressure nearly saturates at sufficiently large values of the viscosity ratio or the droplet radius. These findings are important for an optimal design and enhanced performance of microfiltration systems with slotted pores.