Characterization of the lifespan of an academic paper Every paper has a life-span that could be measured by the time difference between the publication date and the date of the "last" citation (if one exists). Of course, it is not possible for one to predict when the last citation would be, since it is theoretically possible for a paper published 50 years ago with 0 citations till date to be cited by someone tomorrow. 

But the basic idea is: given citation information till date, is there a way to characterize the life-span of an academic publication? Is this a concept that has been studied before?
Yes this has been studied before. One endpoint for what your looking for is the citation half-life.

Basically, this is a metric that calculates the median year age of articles citing a journal. This Science Magazine article discusses the topic further.