Correcting Misconceptions

There are some things that people get wrong about the nature of the obligation:

First, Communion is for the fully initiated.  As discussed above, it requires Baptism and catechesis leading up to one's first communion or an alternative rite of initiation for those already baptized according to the Trinity.  Presently, it also requires religious instruction prior to the reception of those sacraments of initiation.  That said, you are free to go to the altar to receive a blessing.  You do not need to be a Catholic to receive a blessing from a priest.

For those who may commune, you only have to fast one hour prior to consuming Communion.  This is an ecclesiastical discipline, not instituted directly by God, and its specificity is set by the bishops themselves at this moment or that of history.  For most Sunday masses (but not far shorter weekday masses!), this means that you simply have to refrain from eating during Mass.  Unless you are a toddler, that is not very taxing. 

Allowances are always made for medical emergencies or even just basic needs (such as water or medication).  In the olden days, the requirement was more extreme (which is likely where all of the explanations come from).  At one point it was three hours.  At another, it was midnight!  Nowadays, it is only for one hour prior to physically receiving Communion.

Second, fulfilling your Sunday obligation does NOT require the consumption of the Eucharist.  If you cannot commune for whatever reason, you can still do an act of Spiritual Communion.  One such traditional formula is to say:

My Jesus, I believe that You are present in the Most Holy Sacrament. I love You above all things, and I desire to receive You into my soul. Since I cannot at this moment receive You sacramentally, come at least spiritually into my heart. I embrace You as if You were already there and unite myself wholly to You. Never permit me to be separated from You. Amen. 

For those who find these words difficult to say, due to lack of belief in the Real Presence, you must realize that it is something the earliest Church Fathers as taught by St. John the Evangelist did in fact believe. 

The bishop St. Ignatius Martyr (ca. 108 AD) spoke disapprovingly of the Docetist heretics: "[who] abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness, raised up again."  For relative dating of this belief, it is commonly believed by scholars that the disciple John lived through the onset of Trajan's reign and was a direct contact of St. Ignatius and others.

To be sure, belief that Christ did not institute the Eucharist as His own body and blood is a modern development following the Protestant Reformation (and even there, between the Lutherans, the Anglicans, and the Calvinists and many others since, there has never been agreement on what the Eucharist is.).   That lack of coherence says something.

By contrast, despite their various differences (and there are more than many realize), the Apostolic Churches emerging from Rome, Constantinople, Alexandria, Antioch and many other ancient centers of Christianity have consistently preached in favor of the Real Presence.  It is a catholic (small 'c') belief of Apostolic Christianity: the bread and wine are actually Christ's flesh and blood.  This has been one of the few beliefs that unite Coptics and Orthodox and Catholics.  It is also no coincidence that each of these historical churches also has a priesthood to administer these rites.  But the relationship between Sacraments/Mysteries and the Priesthood of Melchizedek is a topic for another day.

My point is not so subtle: by historical standards, it is exceptional not to believe in the Real Presence.  The question then isn't why Catholics believe in It but why other (modern) Western Christians do not.

At this point, I will put a pin in it as we say.

Third, as a courtesy and spiritual discipline, one should always try to get to Mass at least 10 minutes before it begins (in order to compose yourself spiritually).  That said, there are legitimate excuses for arriving late (or even leaving early).  A classic example is traffic delays or car trouble which you could not have anticipated. 

An informal criterion of fulfilling the obligation is such that you should be there before the Gospel is read; and you should leave only after receiving the final benediction from the priest.  If you arrive after the Gospel reading or leave before the blessing, the obligation is generally considered unsatisfied by most modern Catholics in lieu of a legitimate excuse.  That said, I do not know if Canon Law specifies a "cut off" per se.  Some older manuals from the Early Modern period do go on to mention in the explicitness that characterizes much of the post-Tridentine moment that one must be present from the Offertory through the Priest's Communion.  Even so, those sources are not as authoritative as one would think.

The Church as a loving Mother is somewhat lenient to her children but only as far as necessity permits (otherwise, an overly permissive mother does her child a disservice in bringing them up to be spiritually responsible and serious disciples of Christ).  In lieu of guidelines and necessary criteria, discipline is watered down to no limit and discipline thus ceases to exist at all. 

If you find that you are the person who wants to check off the old box and are overly preoccupied with the technicalities of this or that, then you should probably see a spiritual director asap and submit to his direction provided he is both an orthodox and considerate pastor.

A lot of outsiders have mocked Catholics for this "legalist" mindset, but it is really just a practical approach to moderation between two extremes: being too rigorist and too lax.  The institutional Church has rules just as any organization has rules.