The third party doesn’t need to predict it, just repeat it. The relay doesn’t need to understand or modify the message, just pass it along.

If the message is encrypted with some time component and a pre-shared secret then it is protected from a replay attack no?

Yes, but a replay attack is quite different from a relay attack.

Hm, good point. I guess I don't really know how these systems work. I assumed there was some kind of rotating value but I have no reason to believe this. Based on these attacks it seems the keys are really just sending the same signal every time. That appears to be a real shortcoming of the design.

I think you’re not understanding the attack. It could be a unique, unpredictable signal every single time and the relay attack would work just fine. The devices intend to use distance to prevent this, with distance determined by strength of signal. The relay captures the challenge, passes it to the fob and then passes the response back to the car, boosting the signal if necessary. The timing on this is fast enough that it is within the tolerance of the system. As long as these devices are acting as proximity sensors and your fob isn’t electromagnetically isolated, this attack will work. No amount of key rotation will help.

Ok yes, I was confused. Thank you for spelling that out for me, now I understand what is happening.

The modern ones send a unique value each time, so capturing the transmission and playing it back is useless. But that doesn’t save you from an attacker that just amplifies the signal and otherwise lets the two ends communicate normally.