Simulating incompressible fluid dynamics in densely packed microfluidic devices, such as Deterministic Lateral Displacement (DLD) arrays, presents a significant computational challenge. As obstacle density increases, standard iterative solvers often experience severe performance degradation. In this report, we show that this difficulty is intrinsically linked to the pre-asymptotic degradation of the pressure-velocity coupling stability. By analyzing generalized obstacle arrays, we prove that the continuous inf-sup (LBB) constant deteriorates at an exact rate of $\Theta(m^{-1})$, where $m$ represents the obstacle density. This geometric penalty mathematically explains the severe ill-conditioning observed in classical saddle-point solvers.

Guided by this explicit scaling law, we establish a rigorous framework for mitigating the geometric ill-conditioning. Numerical experiments on both standard and highly asymmetric micro-pillar arrays are conducted to validate the theoretical analysis and evaluate the performance of various preconditioning strategies. The results demonstrate that solvers properly adapted to the exact pre-asymptotic limits can achieve robust, density-independent convergence, successfully tackling highly ill-conditioned systems approaching millions of degrees of freedom. This provides a reliable computational foundation for complex microfluidic simulations.