That's probably some sort of gate on your headphones that silences audio (by killing power to the amplifier circuitry) if it's below a threshold loudness level,

That's probably some sort of gate on your headphones that silences audio (by killing power to the amplifier circuitry) if it's below a threshold loudness level, to prevent users from hearing a hissing sound the cheap circuitry produces that is otherwise masked by other louder sounds. When gate opens again, it takes 1-2 seconds for the amplifier to power up completely.