Meaning of "call" in "close call"
Solution 1:
Close call: (the call in this expression derives from the meaning 'decision' in the context of sport)
also, close shave . Narrow escape, near miss. For example, That skier just missed the tree—what a close call , or That was a close shave, nearly leaving your passport behind .
The first phrase (close call) dates from the late 1800s and comes from sports, alluding to an official's decision ( call ) that could have gone either way.
The second ( close shave), from the early 1800s, alludes to the narrow margin between closely shaved skin and a razor cut. (This latter usage replaced the much earlier equation of a close shave with miserliness, based on the idea that a close shave by a barber meant one would not have to spend money on another shave quite so soon.)
(from dictionary.reference.com)
Solution 2:
Beyond the etymology of the idiom, it's just one of those formulaic, commonplace expressions people jut use. Many an idiom and phrasal verb sound very counterintuitive for non-English speakers, but at some point, after living "in the language" for a long time, they take hold and you just use them, in the absence of anything better. I was actually looking for a less corny way of saying "after a few close calls"... For a replacement!