Because River Song is a time traveller herself, her adventures with the Doctor occur out-of-synchronisation; their first meeting (from the audience's perspective) is his first and her last.This reminds me of one of my favourite books, The Sword in the Stone, in which Merlyn lives his life backwards.
Which explains this exchange just after he has met 'the Wart' - the boy who will grow up to become King Arthur:
Merlyn stopped talking and looked at the Wart in an anxious way.
"Have I told you this before?" he inquired suspiciously.
"No," said the Wart. "We only met about half an hour ago."
"So little time to pass as that?" said Merlyn, and a big tear ran down to the end of his nose.The implications of living backwards through time are not seriously explored by White: he just uses it for the occasional throwaway joke.
Still, it makes you wonder if Russell T. Davies or Steven Moffat were thinking of The Sword in the Stone when they invented the character of River Song. It is not a bad influence to have.