The most common and most likely answer to this crossword clue is the 7 plus 2 letter word PRESSED ON
I've seen this crossword clue in The Times
P
R
E
S
S
E
D
O
N
Buddy explains!
The straight part
We know that "kept going" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kept going = pressed on.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.