The most common and most likely answer to this crossword clue is the 5 plus 5 letter word PEARL DIVER
I've seen this crossword clue in The Guardian
P
E
A
R
L
D
I
V
E
R
Buddy explains!
The straight part
We know that "One going down for a long time" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one going down for a long time = pearl diver.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.