"Public/symmetric key cryptography" is just the name of the practice, of course it's doing fine. What's not doing fine is picking a particular set of ciphers/hash functions/signature scheme and expecting to not fail in 40 years.
Now, there are various kinds of hot attacks, such as side channel leaks, that always present a serious challenge in many threat scenarios. And it's certainly possible to have bad implementations of a solid algorithm. But for AES implementations are very mature, and side channel attacks do not apply to data at rest. So in the context of "will my encrypted ciphertext with all my deepest secrets [sitting on a drive/in the cloud/wherever] be crackable in 40 years" no, symmetric-key crypto with 256-bit keys is dependable at this point.
A false sense of defeatism is itself plenty dangerous to security.
To be clear, 2^56 is trivially brute-force-able today, but that can be mitigated with constructs like 3DES, which are still (barely) secure despite being based on a 45-year-old cipher.
(So no one mistakes my intent, there are many reasons to prefer AES over DES. I just wanted to provide it as an example, especially since it happened to line up with the 40-year timeframe.)
Youch, this broke my intuition.
"we’ve built a system with 48 Virtex-6 LX240Ts which can exhaust the keyspace in around 26 hours"
Having to rent thousands of dollars in GPU-hours or using specialized hardware doesn't sound "trivial" to me. Practical, yes. Accessible even to a layman with money to spare, yes. Trivial? Hell no.
If I had some DES-encrypted files that I'd lost the key to, and they were important enough that I needed their contents, I would probably be happy that I could crack the key today and recover them if I spent enough, but doing so would still not be "trivial".
Apparently there's even a SaaS offering to do it for you in some cases (for staggeringly cheap, like $300), but I had no idea that existed when I wrote my comment.
They might BnE your key though, if you aren't careful enough.