The influence of diluted network connectivity and dissipation on the collective dynamics of pulse-coupled oscillators were investigated. It was found that the long chaotic transients dominates the dynamics for a wide range of parameters and become prevalent for large networks. It was also found that the dynamics of the transients exhibit a novel form of robust synchronization. The results show that the structure of a network can have major impact on its dynamics, as small structural changes induce fundamentally different forms of behavior.