In many central pattern generators, pairs of neurons maintain an approximately fixed phase despite large changes in the frequency. The mechanisms underlying phase maintenance are not clear. Previous theoretical work suggested that inhibitory synapses that show short-term depression could play a critical role in this respect. In this work we examine how the interaction between synaptic depression and the kinetics of a transient potassium (A-like) current could be advantageous for phase constancy in a rhythmic network. To demonstrate the mechanism in the context of a realistic central pattern generator, we constructed a detailed model of the crustacean pyloric circuit. The frequency of the rhythm was modified by changing the level of a ligand-activated current in one of the pyloric neurons. We examined how the time difference of firing activities between two selected neurons in this circuit is affected by synaptic depression, A-current and a combination of the two. We tuned the parameters of the model such that with synaptic depression alone, or A-current alone, phase was not maintained between these two neurons. However, when these two components came together, they acted synergistically to maintain the phase across a wide range of cycle periods. This suggests that synaptic depression may be necessary to allow an A-current to delay a postsynaptic neuron in a frequency-dependent manner, such that phase invariance is ensured.