What is your thoughts several factors that may be the cause for a distribution to not appear normal in nature. Perhaps the most important up there on the list, is that 'said' variable just simply isn't normal in nature. A trad'tl example from a textbook might be the following:

• modeling the lifetime of a car battery (Weibull distribution)
• modeling the probability that someone survives past the age of 80 years old (Weibull distribution).

The Weibull distribution can model lifetimes that are not "memoryless". This is a stats distribution more commonly used in engineering or in survival analysis classes.