High-throughput single-cell genomics is used to gain insights into diseases such as cancer. Motivated by this important application, microfluidics has emerged as a key technology for developing comprehensive biochemical procedures for studying DNA, RNA, proteins, and many other cellular components. Recently, a hybrid microfluidic platform has been proposed to efficiently automate the analysis of a heterogeneous sequence of cells. In this design, a valve-based routing fabric based on transposers is used to label/barcode the target cells. However, the design proposed in prior work overlooked defects that are likely to occur during chip fabrication and system integration. We address the above limitation by investigating the fault tolerance of the valve-based routing fabric. We develop a theory of failure assessment and introduce a design technique for achieving fault tolerance. Simulation results show that the proposed method leads to a slight increase in the fabric size and decrease in cellanalysis throughput, but this is only a small price to pay for the added assurance of fault tolerance in the new design.