We usually say that AIs don't sleep and count it as an advantage they have over humans. But this is not entirely true. There can be (long) periods of time when no outputs (or output change) is warranted from the AI. A mobile robot may need to remain static when it recharges its batteries (for example my 3 roombas). There can be extended periods of time during which inputs don't change much (see my blog of 1 March 2013, item number 1). This can be related to periodic variation of the environment (like night time if visual senses are involved). These result in a period of low (or zero) activity for the AI. Of course this may be avoided if a distributed multiagent system is involved.
Even internal activity ("thinking") may sometimes be reduced. There may be times when the AI is organizing/sorting its memory (perhaps to permit faster memory search at future times). Time may be spent finding and resolving conflicts/contradictions in memory. In Asa H time is spent normalizing or renormalizing new or modified case vectors (assuming that a dot product similarity measure is going to be used). Times may also be spent doing things like defragging and garbage collection.
An AI might sleep.