You might make the case that MSA and Classical Arabic is an exception, but MSA is not spoken natively AFAIK. Other than that, I cannot think of any examples where a language spoken by someone a thousand years ago would be intelligible now. Languages change in sound, structure and vocabulary over time naturally. That's how we got the Romance languages from Latin (which is no longer spoken).
However, language standardization artificially slows down change, so current languages might last a lot longer. English hasn't changed that much since Shakespeare and the KJV.
Maybe interesting to you: https://en.m.wikipedia.org/w/index.php?title=Conservative_(l...
Yes, for written form you could make that argument, though there are some differences between the two. Also, it didn't really "last" in the normal sense, since it was revived in modern times.
Also, Tibetan maintains the same spellings from 1200 years ago, but that really just means that it's very, very difficult to spell, since the pronunciation no longer matches spelling well.
These make interesting exceptions to the general rule, so I think the original point is still very valid. I'm curious about old vs. modern Syrian, if anyone knows about that.
