And conversely what would it mean if we never detect gravity waves? Are there any reasonable theories that posit that gravity waves don't exist?
That general relativity is either incomplete or wrong. It would mean that gravity either propagates far more rapidly or far more slowly than we think. Given however that c is considered and so far demonstrably the maximum velocity of information propagation in this spacetime, instantaneous propagation seems unlikely, particularly given the Mercury orbital confirmation. That all said, we may be looking at things naive…
Black holes for example dilate time, and may either not exist (since they take infinite time to form), or may produce gravity waves that are too time dilated (i.e. slow) to detect.