Well, if you did find just one rabbit in the Cambrian, you would probably be better off assuming that the fossil somehow got forced into older rock, or that the dating is wrong, or something, than that the whole theory of evolution comes tumbling down. In fact I'd be surprised if there aren't at least a couple of fossils somewhere whose placement biologists can't currently explain.
But I'm a little more familiar with physics, so I can give what I think is a better example there. Modern physics is faced with some big problems; inconsistency between the standard model and general relativity, dark matter, dark energy... but physicists don't say "oh no, the basics of our theories are refuted, back to square one". They say "we need to refine our model, in some unknown way, and in the meanwhile we'll assume without any theoretical justification that the standard model applies on the atomic scale, general relativity applies on the galactic scale (with the addition of some 'dark' fudge factors), some ad-hoc mix applies to things like black holes, and we don't know what applies on the Planck scale".
I'm not saying that falsifiability isn't, at least, a good thing to have, as a rule-of-thumb. Popper noticed something important. Other people have proposed other demarcations; Lakatos, for example, argued for judging 'research programs' rather than static theories, and that a 'progressive' research program is one that continues to produce novel predictions. Personally, I lean towards the view that there is no way to delimit science and non-science except sociologically; you just have to ask whether something is true or not.
Regardless, the point is, it's a lot more complicated than "no single piece of evidence would cause people to abandon this theory" => "this theory's proponents are not scientists".