A previous study of a single load-unload cycle of an adhesive contact between an elastic-plastic microscopic sphere and a rigid flat is extended here for several load-unload cycles. The interacting forces between the sphere and the flat obey the Lennard–Jones potential. Kinematic hardening is assumed for the sphere material to account for possible plastic shakedown, and the difference between kinematic and isotropic hardenings is discussed. The main goal of the current work is to investigate the evolution of the load-approach curves for the elastic-plastic spherical contact during its cyclic loading-unloading. These curves are presented for different physical conditions, represented by three main dimensionless parameters, which affect the behavior of the elastic-plastic adhesive contact. A transition value of the Tabor parameter is found, below which the load-approach curves are always continuous and jump-in and jump-out instabilities are not expected.