The rare-earth ions (RE = Eu, Dy Ho, Tm, Y) doped charge-ordered antiferromagnetic manganites, Pr_0.45RE_0.05Ca_0.5MnO₃, were studied for the magnetic and the transport properties in the presence of external magnetic fields of up to 14 tesla. Regardless of the intrinsic magnetic property of RE ions, all the compounds exhibit successive step-like metamagnetic transitions at low temperatures, which are strongly correlated to their electronic transitions. At any fixed temperature in two different temperature regimes, we observed contrary effects of the magnetic-field cycling on the resistivity of these manganites, namely, i) in the low temperature regime (≤ 70 K), the resistivity was irreversible showing lower values than initial values after a magnetic-field cycle was over, which is consistent with the irreversible magnetization, and ii) in a temperature regime above 70 K, the resistivity is irreversible with noticeably higher values than initial values, whereas the magnetization was found to be reversible. For the latter case, we further show that this irreversibility of resistivity systematically depends on the temperature and the magnitude of applied magnetic field. These results suggest that the observed resistivity behavior originated from the magnetic-field–induced metamagnetic transitions and training effect.