An incompressible fluid flow model for a thin-film thrust bearing with slip flow is derived, leading to a modified Reynolds equation for a highly rotating rotor that incorporates a slip length shear condition on the bearing faces, extending previous bearing studies for new bearing applications associated with decreasing film thickness. Mathematical and numerical modelling is applied to the coupled process of the pressurized fluid flow through the bearing, with a Navier slip condition replacing a no-slip condition, and the axial motion of the rotor and stator. The derived modified Reynolds equation is coupled with the dynamic motion of the stator through the pressure exerted by the fluid film, with explicit analytical expressions for the pressure and force determined and the equation for the bearing gap reduced to a non-linear second-order non-autonomous ordinary differential equation. A mapping solver is used to investigate the time-dependent bearing gap for prescribed periodic motion of the rotor. A parametric study focuses on bearing operation under close contact motion to examine the minimum film thickness and possibility of bearing face contact.