Strings, Percy thought, were terrible analogies for dying. They implied that death was always sudden and unexpected, like you never knew it was coming until one moment you simply aren't there anymore.
Now, one might ask the question of what would make a seventeen year old boy qualified to determine what did or did not constitute a fitting metaphor for death. And in response to this, Percy would argue that lying bleeding to death on a battlefield, alone and afraid gave him the right to come to such conclusions.
He always remembered when he first saw The Fates cut the string that he thought was his own life. Up until now, he had never thought about them much. However, dying can give you some time to reflect on it all.
The thing about a string, is that it implies that death is always sudden when in actuality, it isn't always. No, Percy much preferred to think of life as a vast expanse of land, on which mankind travels across at different speeds, each passing their own landmarks and creating their own paths. At the end of their journey, they are met with a cliff which they inevitably fall off of. Your time on this planet really just depends on how fast you're running.
Percy had already jumped off his edge he knew, and was simply waiting to hit the bottom. (It isn't the fall that kills you after all, it's the landing.) So, Percy waited. He waited for himself to hit the bottom. And when he finally did, he had no regrets, because Percy ran through his life full speed ahead, and never had any intention of stopping.