We explore the bistability effect in a dimensionally scaled semiconductor nanostruncture consisting of a diluted magnetic semiconductor quantum dot (QD) and a reservoir of itinerant holes separated by a barrier. The bistability stems from the magnetic phase transition in the QD mediated by the changes in the hole population. Our calculation shows that when properly designed, the thermodynamic equilibrium of the scaled structure can be achieved at two different configurations; i.e., the one with the QD in a ferromagnetic state with a sufficient number of holes and the other with the depopulated QD in a paramagnetic state. Subsequently, the parameter window suitable for this bistability formation is discussed along with the the conditions for the maximum robustness/non-volatility. To examine the issue of scaling, an estimation of the bistabiity lifetime is made by considering the thermal fluctuation in the QD hole population via the spontaneous transitions. A numerical evaluation is carried out for a typical carrier-mediated magnetic semiconductor (e.g., GaMnAs) as well as for a hypothetical case of high Curie temperature for potential room temperature operation.