The most common and most likely answer to this crossword clue is the 1 plus 5 plus 4 letter word A SHORT FUSE
I've seen this crossword clue in Financial Times
A
S
H
O
R
T
F
U
S
E
Buddy explains!
The straight part
We know that "propensity to lose temper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case propensity to lose temper = a short fuse.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.