Any help here will be greatly appreciated.

I am trying to simulate laminar flow over a step at Reynolds number 1000. I am using SIMPLE algorithm. I am interested in the time development of the flow. The x velocity is assigned parabolic at the left edge (entrance); y velocity is assigned zero. Pressure is assigned at one node to be 1.0. At the exit, both x and y velocities are allowed to adjust, pressure is assigned 0.0 accross. At all the interior nodes, velocities are pressure are started with zero values.

As the flow develops, a pressure front develops, but soon afterwards the pressure drops to zero in the entire flow field, irrespective of the pressure value assigned at the left node. I have also tried to assign pressure at the entire entry cross-section, with the same result. Obviously, my results are dubious.

Is it coding problem? Formulation problem? Any suggestion would be helpful.

Have only one pressure boundary condition for the domain. You can assign pressure at the outlet boundary to be zero and let the code to calculate the pressure at all other points.