The most common and most likely answer to this crossword clue is the 14 letter word UNFAITHFULNESS
I've seen this crossword clue in The Times
U
N
F
A
I
T
H
F
U
L
N
E
S
S
Buddy explains!
The straight part
We know that "not staying with uncle?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not staying with uncle? = unfaithfulness.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.