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We discovered a hysteresis in a microwave-driven low-pressure argon plasma during gas pressure change across the transition region between $α$ and $γ$ discharge modes. The hysteresis is manifested in that the critical pressure of mode transition depends on the direction of pressure change. As a corollary, the plasma would attain different discharge properties under the same operating parameters (pressure, power, and gas composition), suggesting a bi-stability or existence of memory effect. Analysis of the rotational and vibrational temperatures measured from the OH (A-X) line emissions shows that the hysteresis is mainly due to the fast gas heating in the $γ$-mode leading to a smaller neutral density than that of the $α$-mode. When increasing the gas pressure, the $γ$-mode discharge maintains a relatively higher temperature and lower neutral density, and thus, it requires a higher operating pressure to reach the $α$-mode. On the other hand, decreasing the pressure while maintaining $α$-mode, the transition to $γ$-mode occurs at a lower pressure than the former case due to a relatively higher neutral density of $α$-mode discharge. This interpretation is supported by the fact that the hysteresis disappears when the plasma properties are presented with respect to the neutral gas density instead of pressure.