As you know the auto shutoff level gives a rough estimate of the total energy left in a simulation as a fraction of the total injected energy. If the device is operating close to the resonant frequency, it takes a relatively longer time for the energy to decay to the default auto shutoff level and it can also keep oscillating for a long time as you have seen. As long as this level reduces (and doesn't exponentially increase), it should not be a concern. Also, this doesn't always depend upon how big the structure is but how close it is to the resonant frequency. Sometimes even when really small structures are excited by their resonant frequency, they tend to take a lot longer to simulate and you can also see this oscillatory behavior. This can be most commonly observed in resonators.
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