Thomas Aquinas's take on transsubstantiation supposes that the accidents of bread and wine can continue existing even after the bread and wine have perished, something that was heavily criticized by people like Jan Hus.
But here is an argument for the possibility of an accident outliving its substance. Consider a very long rattlesnake, stretching out to maybe ten million kilometers in length. The rattlesnake is rattling for one second. The rattling of the tail is an accident of the rattlesnake, call this accident R. Then the snake is near-instantaneously destroyed, e.g., by a series of synchronized explosive charges.
Well, near-instantaneously in one reference frame! This snake is long enough that there will be another reference frame in which the front half is destroyed 15 seconds before the back half is. In this reference frame, there will be a time when the rattling of the tail occurs even though the front half of the snake doesn't exist. But a snake whose front half has been destroyed is no longer existing. So in this reference frame the accident R exists even though the snake no longer does.
Granted, in the case of the snake it is only true in some reference frames that the snake doesn't exist while R does, while in the Eucharist the persistence of the accidents past the demise of the bread and wine takes place in all reference frames. But once we have seen that the principle that accidents must be contemporaneous with their substance is not generally true, I think some wind is taken out of the objector's sails.