This paper investigates the effects of the inlet turbulence intensity (ITI) on the dynamics of a bluff-body stabilized flame operating very close to its blow-off condition. This work is motivated by the understanding that more stringent regulations on combustion-generated emission have forced the industry to design combustion systems that operate at very fuel-lean conditions. Combustion at very lean conditions, however, induces flame instability that can ultimately lead to flame extinction. The dynamics of the flame at lean conditions can therefore be very sensitive to boundary conditions. Here, a numerical investigation is conducted using Large Eddy Simulation method to understand the flame sensitivity to inlet turbulence intensity. Combustion is accounted for through the transport of chemical species. The sensitivity to inlet turbulence is assessed by carrying out simulations in which the inlet turbulence is varied in increments of 5%. It is observed that while the inlet intensity of 5% causes blow-off, further increased to 10% preserves a healthy flame on account of greater heat release arising from greater and balanced entrainment of combustible mixtures into the flame zone just behind the bluff-body. This balanced stabilization is again lost as the inlet turbulence intensity is further increased to 15%. Since experimental data pertaining to the topic of this paper are rare, the reasonableness of the combination of models is first checked by validating Volvo propane bluff-body flame, whereby reasonable agreement is observed. This study will advance our understanding of the sensitivity of bluff-body flames to boundary conditions specifically to the inlet turbulent boundary condition at near critical blow-off flame conditions.