Arcane Echo enchantment question

So arcane echo is listed as an enchantment. But I'm not sure how its enchantment status works.

Is it an enchantment (i.e you're under an "arcane echo" enchantment) until you cast another spell or is it an enchant until the spell you echo disappears?

If it's the first does that mean someone can remove the echo before you have a chance to copy a spell? If it's the second does that mean someone can remove the copied spell after you've echoed it?

Great, thanks for the amazingly quick reply!