Have you noticed, it is impossible to be conscious outside of the present moment. We cannot be conscious in the past or in the future. Consciousness is this ever-present entity within us. In this sense, consciousness is not really within time, as we normally understand the term. What is, however, only within time, only temporary, temporal, and impermanent, is everything that is contained in our phenomenal world. Our physical bodies are impermanent. Desires, emotions, feelings, and thoughts, which together form our psyche, are impermanent. Our personality is an impermanent thing, always changing, from one moment to the next. All these things are passing, are always somewhere between a birth and a death, an arising and a decline, their beginning and their end, their emerging manifestation and final disappearance.
However, consciousness isn't a passing phenomenon. What it can be conscious of is passing, but not consciousness itself. It does not exist as something that is in a constant state of change, somewhere between a phenomenal arising and disappearance. It is eternal. Not in the sense of never-ending time, but rather, in the sense of something that always IS what it IS. Its nature doesn't change. It is the constant changes observed in the phenomenal world that create the impression that time is passing. But again, consciousness is not of time, since it is not something that changes per se. Consciousness remains ever what it is, and exists only in the (eternal) present.