We reinvestigate the generation and accumulation of magnetic flux in optically thin accretion flows around active gravitating objects. The source of the magnetic field is the azimuthal electric current associated with the Poynting-Robertson drag on the electrons of the accreting plasma. This current generates magnetic field loops which open up because of the differential rotation of the flow. We show through simple numerical simulations that what regulates the generation and accumulation of magnetic flux near the center is the value of the plasma conductivity. Although the conductivity is usually considered to be effectively infinite for the fully ionized plasmas expected near the inner edge of accretion disks, the turbulence of those plasmas may actually render them much less conducting due to the presence of anomalous resistivity. We have discovered that if the resistivity is sufficiently high throughout the turbulent disk while it is suppressed interior to its inner edge, an interesting steady-state process is established: accretion carries and accumulates magnetic flux of one polarity inside the inner edge of the disk, whereas magnetic diffusion releases magnetic flux of the opposite polarity to large distances. In this scenario, magnetic flux of one polarity grows and accumulates at a steady rate in the region inside the inner edge and up to the point of equipartition when it becomes dynamically important. We argue that this inward growth and outward expulsion of oppositely-directed magnetic fields that we propose may account for the approx. 30 min cyclic variability observed in the galactic microquasar GRS1915+105.