Extensive classical investigation of the vibrational predissociation dynamics of the model He ... Br-2 and Rg ... I-2 (Rg=He, Ne, and Ar) van der Waals complexes is performed. Classical trajectory calculations of the fragmentation rates are accomplished with the numerical analysis of the phase-space structure within the two-dimensional T-shaped model. Various bifurcations of the phase portrait with increasing excitation energy are found to produce a remarkable effect on the fragmentation dynamics causing irregular variations of the decay rate. This effect is proven to be quite persistent and pertinent to the more realistic three-dimensional dynamics as well. The implications of the results for studying quantum-classical correspondence for metastable states are indicated.