According to Susan Blakemore, awareness is a moment-to-moment phenomenon (2002, p. 26).
It is the result of instantaneous perception, that can be repetitive, but in a discontinuous manner.
Moreover awareness is always awareness of "something". It necessarily supposes an experience of some event "there outside". But the experience is "inside" as it is basically a complex computation process in a neural network.
It is also automatic. We do not need to decide that we are going to perceive: we just do.
As our nervous system possesses somehow the faculty of remembering former experiences we easily gain the impression of a continuity of consciousness. In fact it seems that this is also a construction in our nervous system which somehow throws bridges between these discontinuous moments of awareness.
The nature of the bridges is probably related to the continuous existence of a neuronal net in our brain, which becomes repeatedly reorganized after each experience. this is the gist of Maturana and Varela concept of Autopoiesis.(see J. Gran, 2002, p. 46-49)