It really depends on the technology. It will last until the NSA finds a way to crack it. They will probably be able to crack this the same way that bittottent was cracked. By inserting nodes into the network that recorded the data going through. Get enough nodes under your control, then you can potentially piece together whole conversations. It is a difficult and costly process. It's a cat and mouse game. The same one that happened in WWII. Bletchley Park cracks the Enigma. Germany adds another rotor. Bletchley cracks that. Make it complex enough, you can buy yourself some time.
I assume you mean Tor. And, a prerequisite of being "NSA-Proof" is being open source. If it's closed, you can assume that it's just a honeypot, not secure, etc. Hell, even if it IS open source, we all saw what happened with OpenSSL. At least heartbleed eventually got identified and patched.They will probably be able to crack this the same way that bittottent was cracked. By inserting nodes into the network that recorded the data going through. Get enough nodes under your control, then you can potentially piece together whole conversations. It is a difficult and costly process.