For example, let's say that I went to sleep one night at 5:00 am. Out of exhaustion, I would most likely sleep until the late afternoon. Since I woke up so late, I wouldn't be tired until very early in the morning, maybe 5:00 am again. This pattern would repeat over and be hard to break out of. My question is, what would we call this type of pattern? Another example would be smoking; you begin to smoke and it's very hard to stop. I'm not looking for "addiction", because that implies that I am physically and mentally dependent on the object.
The apt term for this is vicious circle or vicious cycle. According to NOAD, the definition goes thus:
a sequence of reciprocal cause and effect in which two or more elements intensify and aggravate each other, leading inexorably to a worsening of the situation.
In your own words: This pattern would repeat over [and over] and be hard to break out of. I cannot think of a better phrase than vicious cycle.
You might use self-sustaining or feedback loop.