Guilin Sun
Ansys Employee

This is most likely that such device has some strong  resonance, which needs long time for the resonant signal to decay.

If you do not need very accurate transmission and reflection at the resonance, you can use "time apodization" in the monitor.

Please also check if the PML is thick enough. Occasionally PML may also cause fake resonance. However in such case changing the simulation span the resonace will shift, which can be differentiated from the real resonance.

Please refer to this post for more: 

Ansys Insight: Slow convergence in FDTD