The Bible plainly rules out the notion of Jesus being “re-sacrificed”:

Hebrews 7:27 (RSV) He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people; he did this once for all when he offered up himself. (cf. 9:12)

Hebrews 9:24-26 For Christ has entered, not into a sanctuary made with hands, a copy of the true one, but into heaven itself, now to appear in the presence of God on our behalf. [25] Nor was it to offer himself repeatedly, as the high priest enters the Holy Place yearly with blood not his own; [26] for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the age to put away sin by the sacrifice of himself. (cf. 9:27-28)

The crucifixion was a one-time historical event. We must keep in mind, however, that Jesus is God. He was subject to time in His human nature, but in His Divine Nature, He is outside of time. Jesus is called “a priest for ever”: not for six hours on the cross only:

Hebrews 5:6 as he says also in another place, “Thou art a priest for ever, after the order of Melchiz'edek.” (cf. 6:20; 7:24)

Thus, the Apostle John referred to Jesus in heaven (after His resurrection and ascension) as “a Lamb standing, as though it had been slain”:

Revelation 5:6 And between the throne and the four living creatures and among the elders, I saw a Lamb standing, as though it had been slain, with seven horns and with seven eyes, which are the seven spirits of God sent out into all the earth; (cf. Heb 8:1; 9:24 above)

In this sense, the one crucifixion is “eternally present” and supernaturally “brought to us” in the Sacrifice of the Mass. The texts refer to the definitive, end-all nature of the crucifixion, but not to some solely natural, timebound analysis of it. The Council of Trent (Session 22, Chapter II), stated:

And forasmuch as, in this divine sacrifice which is celebrated in the mass, that same Christ is contained and immolated in an unbloody manner, who once offered Himself in a bloody manner on the altar of the cross; the holy Synod teaches, that this sacrifice is truly propitiatory and that by means thereof this is effected, that we obtain mercy, and find grace in seasonable aid, . . . For the victim is one and the same, the same now offering by the ministry of priests, who then offered Himself on the cross, the manner alone of offering being different. The fruits indeed of which oblation, of that bloody one to wit, are received most plentifully through this unbloody one; so far is this (latter) from derogating in any way from that (former oblation).

First of all, there is the differentiation (first sentence) between “unbloody manner” and “once offered Himself in a bloody manner on the altar of the cross” – thus showing that the former is not regarded as the latter, repeated over and over again (as the contra-Catholic reasoning would claim), but rather, a different means of bringing the one sacrifice to us.

Secondly, there is the phrase, “the manner alone of offering being different,” thus showing that it is one sacrifice being re-presented (different “manner”).

Moreover, the phrase, “The fruits indeed of . . . that bloody one to wit, are received most plentifully through this unbloody one” shows that the reference was back to Calvary, whose benefit accrues to those partaking of Holy Communion, not to some imagined “repeated bloody sacrifice.”

To drive home the point in a different way, the council reiterates, “so far is this (latter) from derogating in any way from that (former oblation).” The plain language of Chapter I reiterates this:

He, therefore, our God and Lord, though He was about to offer Himself once on the altar of the cross unto God the Father, by means of his death, there to operate an eternal redemption; nevertheless, because that His priesthood was not to be extinguished by His death, in the last supper, on the night in which He was betrayed, – that He might leave, to His own beloved Spouse the Church, a visible sacrifice, such as the nature of man requires, whereby that bloody sacrifice, once to be accomplished on the cross, might be represented, . . . declaring Himself constituted a priest for ever, according to the order of Melchisedech, . . .

Perhaps the language of Trent was not as careful and precise as it should be (one can always argue about style and content of words), but I think a reasonable reading of it arrives at the conclusions that Catholics hold, and have always held.

Another important factor in all this is the lack of understanding of the patristic background. The notion of eucharistic sacrifice (in the Catholic sense) was common in the Church fathers' writings. Thus, one might misinterpret what Trent expressed, and come up with the notion of “sacrificed again and again”. But if the patristic background is known, then it is seen as merely further development of what had been believed long since.

As a man, Jesus' sacrifice was in time and history. As God, outside of time (from that perspective), it is not. His being God brings in a “supra-historical” aspect in which time is transcended. This is what Protestants often seem to neglect. If Jesus is our high priest forever, He is still offering Himself, out of time, because that's what priests do. Otherwise, what is the “pure offering” of Malachi 1:11?

If His Body and Blood are truly present in the Eucharist, then the sacrifice on the cross also must be present in some sense, since that is where the sacrifice took place, and why we talk about Body and Blood at all. One can't be separated from the other.