To put it simply: I always am but I'm not always aware of that. This can be observed when transitioning from dreamless deep sleep (down state) to e.g. REM. But also during meditation, or while doing psychedelics (which is a hit or miss, however), and similar methods. Another way to put it is that awareness of absence is not absence of awareness.

Naturally, "I" denotes the subject or consciousness "thanks" to which every thing is known and who I actually am. And it's the same "I" which you refer to when you denote yourself as "I". The rule of thumb is that if I can observe something, it cannot be I.