Yes, the battery has a life span of a few years for moderate use. Usually, the battery will lose considerable capacity after 500-600 cycles. There is another thread on this battery issue: https://www.allaboutgalaxynote.com/topic/note-battery-issue/
In most regions, the warranty for battery is only 6 months (while the note normally has one year warranty).
So, you may try to get a new battery if you used it heavily before.