This is even worse than a relay attack, since AFAIK those require being near the fob and there are other mitigations (even simple things like timing how long it takes to get a response). This attack essentially lets you clone key fobs permanently, not just start a car while the owner is on the other side of a parking lot. And the encryption would work a heckuva lot better if the attacker had to precalculate every challenge and response with, for example 256 bit AES keys instead of 40 bit keys with 24 bit responses.

You should use a key exchange protocol like Diffie Hellman