The most common and most likely answer to this crossword clue is the 8 letter word WHEEZING
I've seen this crossword clue in The Times
W
H
E
E
Z
I
N
G
Buddy explains!

The straight part
We know that "breathing problem?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case breathing problem? = wheezing.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.
What does WHEEZING mean?
WHEEZING verb- To breathe hard, and with an audible piping or whistling sound, as persons affected with asthma.
- The quality or symptom of breathing with an audible wheeze