The predissociation dynamics of hydrogen chloride ions (HCl+ and DCl+) in the electronic A (2)Sigma(+) state has been investigated by solving the time dependent Schrodinger equation. The predissociation lifetime is shown to strongly depend on the vibrational and the rotational quantum number, with quasi-periodic oscillations. Rovibronic states, which exhibit lifetimes about I order of magnitude larger than those of neighboring states, are termed rotational islands of stability (RIS). These RIS can be correlated with characteristic reference energies, e.g., the difference between rovibronic eigenenergy and the energy of crossing of rotronic bound and repulsive potentials. The origin of these RIS is illustrated by model studies of the positions of the nuclear wave functions involved.