What are the reasons for the Catholic Church's law regarding the Communion fast?

Fr. William P. Saunders of Catholic Straight Answers gives the following reasons for fasting before Communion:

The most important point regarding this question concerns why we ought to [ever] fast. St. Paul reminds us, "Continually we carry about in our bodies the dying of Jesus, so that in our bodies the life of Jesus may also be revealed" (II Cor 4:10). We, too, are charged to convert our whole lives — body and soul — to the Lord. This conversion process involves doing penance — including bodily mortification like fasting — for our sins and weaknesses, which in turn strengthens and heals us. Pope Paul VI exhorted the faithful in his apostolic constitution "Paenitemini" (1966), "Mortification aims at the 'liberation' of man, who often finds himself, because of concupiscence, almost chained by his own senses. Through 'corporal fasting' man regains strength, and the wound inflicted on the dignity of our nature by intemperance is cured by the medicine of a salutary abstinence."

Moreover, the fast before receiving holy Communion creates a physical hunger and thirst for the Lord, which in turn augments the spiritual hunger and thirst we ought to have. In the Old Testament, fasting prepared individuals to receive the action of God and to be placed in His presence. For instance, Moses (Ex 34:28) fasted 40 days atop Mount Sinai as he received the Ten Commandments, and Elijah (I Kings 19:8) fasted 40 days as he walked to Mount Horeb to encounter God. Similarly, Jesus Himself fasted 40 days as He prepared to begin His public ministry (Mt 4:1ff) and encouraged fasting (Mt 6:16-18). Likewise, this corporal work enhances the spiritual disposition we need to receive Christ in the Blessed Sacrament. In a sense, we fast so as not "to spoil our appetite" but to increase it for the sharing of the paschal banquet. Jesus said in the beatitudes, "Blest are they who hunger and thirst for holiness; they shall have their fill" (Mt 5:6). In all, fasting is an exercise of humility, hope and love — essential virtues in preparing ourselves to receive the holy Eucharist.

Fr. John Dietzen makes a similar statement in an editorial in the Catholic Courier, in which he recounts the ways the fasting requirement has loosened through the centuries:

Older Catholics will remember that for centuries total fast from all food and liquids was required from midnight until receiving the Eucharist. ... At the end of the third council session in 1964, Pope Paul VI considerably simplified the eucharistic fast. According to his 1964 decree, people should fast from food and liquids for one hour before receiving Communion. Water does not break the fast and may be taken anytime. The same goes for medications. ... The reason this modified regulation is still on the books is that it can aid in preparing oneself spiritually and mentally for participating in the offering of the Eucharist at Mass and for receiving Communion.

In chapter 6 of Letter 54 (to Januarius) Augustine deals with the question of whether, since Jesus instituted the sacrament during supper, it is proper to make a rule contrary to those circumstances:

It is clear that when the disciples first received the body and blood of the Lord, they had not been fasting. Must we therefore censure the universal Church because the sacrament is everywhere partaken of by persons fasting? Nay, verily, for from that time it pleased the Holy Spirit to appoint, for the honour of so great a sacrament, that the body of the Lord should take the precedence of all other food entering the mouth of a Christian; and it is for this reason that the custom referred to is universally observed. For the fact that the Lord instituted the sacrament after other food had been partaken of, does not prove that brethren should come together to partake of that sacrament after having dined or supped, or imitate those whom the apostle reproved and corrected for not distinguishing between the Lord's Supper and an ordinary meal. The Saviour, indeed, in order to commend the depth of that mystery more affectingly to His disciples, was pleased to impress it on their hearts and memories by making its institution His last act before going from them to His Passion. And therefore He did not prescribe the order in which it was to be observed, reserving this to be done by the apostles, through whom He intended to arrange all things pertaining to the Churches. Had He appointed that the sacrament should be always partaken of after other food, I believe that no one would have departed from that practice.

It is important to note that 1 Corinthians 11 itself deals with abuses stemming from the feasts surrounding Communion. The feasts were not mandated anywhere in Scripture, and were banned by the church at the 363 Council of Laodicea according to Haydock's commentary on verse 21. Continuing on from where we left off, Augustine even conjectures that Paul himself banned the feasts when he visited Corinth:

But when the apostle, speaking of this sacrament, says, "Wherefore, my brethren, when you come together to eat, tarry one for another: and if any man hunger, let him eat at home; that you come not together unto condemnation," he immediately adds, "and the rest will I set in order when I come." (1 Corinthians 11:33-34) Whence we are given to understand that, since it was too much for him to prescribe completely in an epistle the method observed by the universal Church throughout the world, it was one of the things set in order by him in person, for we find its observance uniform amid all the variety of other customs.

I was going to include some quotes from Haydock, but for the most part he just echoes Augustine.