  Magnetohydrodynamic simulations have shown that a non-unique critical
Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which
threshold Sweet-Parker type stationary reconnecting configurations become
unstable to a fast tearing mode dominated by plasmoid generation. It is known
that the flow along the sheet plays a stabilizing role, though a satisfactory
explanation of the non-universality and variable critical Lundquist numbers
observed is still lacking. Here we discuss this question using 2D linear MHD
simulations and linear stability analyses of Sweet-Parker type current sheets
in the presence of background stationary inflows and outflows at low Lundquist
numbers ($S\le 10^4$). Simulations show that the inhomogeneous outflow
stabilizes the current sheet by stretching the growing magnetic islands and at
the same time evacuating the magnetic islands out of the current sheet. This
limits the time during which fluctuations which begin at any given wave-length
can remain unstable, rendering the instability non-exponential. We find that
the linear theory based on the expanding-wavelength assumption works well for
$S$ larger than $\sim 1000$. However we also find that the inflow and location
of the initial perturbation also affect the stability threshold.
