Since beginning of the anime, when he fought Zabuza, he used his Sharingan, and he was out for around one week due to overuse. However, two years later, he's able to use the Kamui often.
How he was able to master the Sharingan in those two years, when he's had it for about decade?
Besides the fact hat Kakshi is Hailed as a prodigy, because of his great intelligence, skill, and aptitude.
This is due Kakashi training in his area of weaknesses. It is not that he did not already master the Sharingan ( Itachi Uchiha even stated that Kakashi was far more proficient of a eye user then most of the natural eye users)
Kakashi's primary weakness was his average reserves of chakra and stamina, As stated on the wiki the usage of the eye requires allot of chakra.To counter that Kakashi possesses very refined chakra control, allowing him to use multiple techniques quickly with the minimum necessary chakra and to their highest level. Kakashi's control also allows him to perform various techniques, usually lightning-based, with few to no hand seals.
On the wiki it is also said
Over the course of the series, his reserves improved considerably to extend his timespan and versatility to fight multiple high-level opponents.
With this information we can conclude that he has increased his chakra pool/ efficieny during combat/training to the point that he can maintain several eye uses and can combat many high level enemys before depleting his chakra pool.
For a side note. During the war Kakashi also could use near to infinite eye attacks when he had Naruto's bijuu chakra attached to him.
