What happened to Frodo's sword?

Question

In 'A Knife in the Dark', Frodo slashes at the Black Rider. Later in the Book, it is said that no weapons can harm the Nazgûl and survive. Why didn't Frodo's blade melt? He still has it afterwards, as it breaks at the ford of Bruinen.
Or did Frodo not touch the Nazgûl with it, so it didn't melt?

Answer 1

Because he didn't actually hit the Nazgûl:

'Look!' he [Strider] cried; and stooping he lifted from the ground a black cloak that had lain there hidden by the darkness. A foot above the lower hem there was a slash. 'This was the stroke of Frodo's sword,' he said. 'The only hurt that it did to his enemy, I fear; for it is unharmed, but all blades perish that pierce that dreadful King.'

So Frodo slashed the Witch-King's cloak, but didn't actually hit anything else.