The most common and most likely answer to this crossword clue is the 6 letter word LASTED
I've seen this crossword clue in The Times
L
A
S
T
E
D
Buddy explains!

The straight part
We know that "went on and on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went on and on = lasted.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 LASTED mean?
LASTED verb- To perform, carry out.
- To endure, continue over time.
- To hold out, continue undefeated or entire.
- To shape with a last; to fasten or fit to a last; to place smoothly on a last.