Though the Feast of the Elevation of the Honorable Cross is one of the Twelve Great Feasts of the Church, it is observed with a strict fast. Why?
According to the Holy Fathers, "the Feast of the Exaltation of the Honorable Cross is equal to that of Great and Holy Friday". With the Cross being raised before us on September 14th, we remember the Crucifixion of Christ for our sins.
But do we fast because of the Cross? No, as St. John Chrysostom explains to those who ask why we keep the fast during Great Lent:
So if a Jew or pagan ask you why you are fasting, do not tell him that it is because of Pascha or because of the mystery of the Cross. If you tell him that, you give him an ample grip upon you. Tell him we fast because of our sins and because we are going to approach the Mysteries. Pascha is not a reason for fasting or grief; it is a reason for cheerfulness and joy. The Cross has taken away sin; it was an expiation for the world, a reconciliation for the ancient enmity. It opened the gates of heaven, changed those who hated into friends; it took our human nature, led it up to heaven, and seated it at the right hand of God's throne. And it brought to us ten thousand other blessings. (Against the Judaizers, Homily 3)
So we do not fast today because of the Cross of Christ, which has been for us a source of blessings, but because of our sins.
It is also because of our sins that we chant continuously "Lord, have mercy!" during the elevation ceremony. This is a further humble reminder to us that the Lord endured the Cross on behalf of our sins, and it reminds us also of our Holy Baptism when we died with Christ in the font and rose with Him when we emerged from the font - yet we continued in our sins. As Sergei V. Bulgakov explains:
"Lord, have mercy"! The holy Church exclaims repeatedly, seeing the elevation of the Cross of the Lord. So it is good to pray and for each of us to see the descent to the depths and ascent to the heights of the Cross of Christ. And from each of us in the paradise of innocence, came out of the holy Baptism font justified and purged from the ancestral sin. There each of us was even in spiritual paradise when with a broken heart we confessed our sins before God and with awe partook of the divine Body and Blood of Christ for the remission of sins. But we lose the first gift of renewal and rebirth in the new life by trespassing the commandments of the Lord, and we often sell the second gift of justification and communion in eternal life for every sweet sin. This humiliation of heavenly honor and glory of the children of God because of our sins, this sinful disgrace, this fall from the God-pleasing heights to the thoughtless similarity to cattle should be seen in our mind in view of the descent to the depths of the Cross of Christ, and we should be distressed in our hearts and sing with all our being: "Lord, have mercy"! And as to each of us the Lord prepared that glory which He had from His Father before the addition of the world, if, according to our sins, we shall not deprive ourselves this glory; and for each of us He prepared a place in the house of the heavenly Father if, willingly and without any reservation, we shall not expel ourselves from the house of the Father, similarly to the prodigal son. Our mind should think that and about this highest glory, seeing the raising of the Cross of the Lord to the heights. And we should kindle and implant in ourselves the decision to aspire with all our soul to become worthy of the high mansions in the house of the heavenly Father and from the depths of our heart sing to the Lord and the Master of our life: "Lord, have mercy"!