The most common and most likely answer to this crossword clue is the 3 plus 6 letter word AIR MISSES
I've seen this crossword clue in Independent
A
I
R
M
I
S
S
E
S
Buddy explains!
The straight part
We know that "Near-disastrous events" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case near-disastrous events = air misses.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.