Space-time digital holography (STDH) maps holograms in a hybrid space-time domain to achieve extended field of view, resolution enhanced, quantitative phase-contrast microscopy and velocimetry of flowing objects in a label-free modality. In STDH, area sensors can be replaced by compact and faster linear sensor arrays to augment the imaging throughput and to compress data from a microfluidic video sequence into one single hybrid hologram. However, in order to ensure proper imaging, the velocity of the objects in microfluidic channels has to be well-matched to the acquisition frame rate, which is the major constraint of the method. Also, imaging all the flowing samples in focus at the same time, while avoiding hydrodynamic focusing devices, is a highly desirable goal. Here we demonstrate a novel processing pipeline that addresses non-ideal flow conditions and is capable of returning the correct and extended focus phase contrast mapping of an entire microfluidic experiment in a single image. We apply this novel processing strategy to recover phase imaging of flowing HeLa cells in a lab-on-a-chip platform even when severely undersampled due to too fast flow while ensuring that all cells are in focus.