Why doesn't Kakashi use his copy ability that often? Kakashi is known as "the copy cat ninja". The Ninjas from the other countries call Kakashi the Copy Cat Ninja because of his Sharingan and how he uses it for his advantage (Copying moves). But he does not use his power to copy very often (or at least not anymore). It is only shown around 3-4 times that he actually copies and uses it against somebody.

Why does he not use this power more often?
What everyone was saying was partially correct. The Sharingan is a kekkei-genkai made for the Uchiha Clan. Since Kakashi isn't native to this clan, he's only able to use his Sharingan after once in awhile. As said before, he used it in the beginning of the series and was out for about a week or two from using too much chakra.

Consumption of all of your chakra will cause you to die.

Now with his Mangekyo Sharingan, he cannot use it much. The example that comes quickly to my head is when Kakashi and Naruto were chasing Deidara during the Gaara Retrieval arc. Kakashi specifically quoted that, "We have to end this soon. I can only activate the Mangekyo probably one more time."

In the current manga, he can only keep up with using his Mangekyo Sharingan with the help from the Kyuubi's aura/chakra.

It consumes way too much chakra for him.