At least as traditionally philosophically understood, the Catholic understanding of transsubstantiation insists on the persistence of (at least some) of the accidents of bread and wine after the bread and wine have ceased to exist. But how can accidents exist without their substance?
Well, imagine a very long rattlesnake—say, a billion kilometers long—all stretched out in space. Suppose that the snake rattles its rattle at noon for a second, and one second after the end of the rattling a prearranged array of blasters simultaneously annihilates the whole snake.
Let R be the accident of the snake's rattling. A simple relativistic calculation shows that there is an inertial reference frame in which the rattling occurs after the vast majority of the snake—including all of the snake's vital organs (which I assume are placed much as in a normal snake)—has been annihilated. But an animal is dead, and hence non-existent (barring afterlife for animals; let's stipulate there is none), after all its vital organs have been annihilated. Thus, there is a reference frame in which the accident R exists after the substance S of the snake has been annihilated.
So special relativity gives us good reason to think that accidents can survive the destruction of the substance, at least in some inertial reference frames. But all inertial reference frames are supposed to be on par.
I suppose an opponent of transsubstantiation could insist that while an accident can survive the destruction of a substance in some reference frames, it cannot survive the destruction of the substance in all reference frames (as it would have to in the case of the Eucharist). But that requirement sounds a little ad hoc.
So, relativity theory gives us good reason to reject one of the most famous objections to transsubstantiation.