Apparently, it is still valid. If you can read Spanish and you have a stomach for legalese, you can try to digest this. It is a relatively long but definitely dull exposition on what you should do in case that you wanted to prove your status of "hidalgo" in modern XXIth century Spain. I've browsed diagonally the document, and the TL;DR; version of if (Disclaimer: Too Boring; Didn't Read All) is that there is no provision of a legal sure path to do so, but they can't find any law against it.
So it seems that it lasted until the end, so is, until the whole hidalguía concept was revoked with the advent of liberalism in the first third of the XIXth century. "Hidalgo" may mean noble, but it was used mainly to refer to nobles without a title. The privileges of hidalgos were few and came to none before the XIXth century, so when the Constitutions of 1812 and 1837 abolished social classes and proclaimed that every citizen was equal before the law being a hidalgo was already useless. Nobility has not been forbiden, though, and since we still have Counts and Marquesses we could have hidalgos too, but in a time where even being a Duke is worthless unless you are also rich (which, incidentally, it's still always the case), what's the point of being an hidalgo?
*Notice that, as Carlos Martin says in the comment, it was not all the modern Basque Country who could claim the privilege. You could claim your hidalguía through several means, but the best ones (the ones nobody would dispute against) were three:
- La Real Carta Ejecutoria de Hidalguía
- La Real Provisión de un mismo acuerdo
- La Real Carta de Vizcainía
The third one, La Real Carta de Vizainía, is the one you are asking for. Several domains of Biscay granted hidalguía automatically to all its naturals, but this doesn't cover all the Basque Country.