Persistent plasma upflows were observed with Hinode’s EUV Imaging Spectrometer (EIS) at the edges of active region (AR) 10978 as it crossed the solar disk. We analyze the evolution of the photospheric magnetic and velocity fields of the AR, model its coronal magnetic field, and compute the location of magnetic null-points and quasi-sepratrix layers (QSLs) searching for the origin of EIS upflows. Magnetic reconnection at the computed null points cannot explain all of the observed EIS upflow regions. However, EIS upflows and QSLs are found to evolve in parallel, both temporarily and spatially. Sections of two sets of QSLs, called outer and inner, are found associated to EIS upflow streams having different characteristics. The reconnection process in the outer QSLs is forced by a large-scale photospheric flow pattern which is present in the AR for several days. We propose a scenario in which upflows are observed provided a large enough asymmetry in plasma pressure exists between the pre-reconnection loops and for as long as a photospheric forcing is at work. A similar mechanism operates in the inner QSLs; in this case, it is forced by the emergence and evolution of the bipoles between the two main AR polarities. Our findings provide strong support to the results from previous individual case studies investigating the role of magnetic reconnection at QSLs as the origin of the upflowing plasma. Furthermore, we propose that persistent reconnection along QSLs does not only drive the EIS upflows, but it is also responsible for a continuous metric radio noise-storm observed in AR 10978 along its disk transit by the Nanc¸ay Radio Heliograph.