Recent experimental data at GSI on the rates of the number of daughter ions, produced by the nuclear K-shell electron capture (EC) decays of the H-like ions 140Pr58+ and 142Pm60+, suggest that they are modulated in time with periods T_{EC} approximately 7 sec and amplitudes a_{EC} approximately 0.20. Since it is known that these ions are unstable also under the nuclear positron (beta;{+}) decays, we study a possible time dependence of the nuclear beta;{+}-decay rate of the H-like 140Pr58+ ion. We show that the time dependence of the beta;{+}-decay rate of the H-like 140Pr58+ ion as well as any H-like heavy ions cannot be observed.