Q:

Does 1 Corinthians 9:27 contradict the doctrine of "The Perseverance of the Saints?"

At First Corinthians 9:24-27, the Apostle Paul writes:

Do you not know that in a race all the runners run, but only one receives the prize? So run that you may obtain it. Every athlete exercises self-control in all things. They do it to receive a perishable wreath, but we an imperishable. So I do not run aimlessly; I do not box as one beating the air. But I discipline my body and keep it under control, lest after preaching to others I myself should be disqualified.

How is this verse understood by people who believe in the doctrine of perseverance, such as those in the Reformed tradition?

A:

Let's compare what Paul said in the Greek with a consideration of the doctrine of perseverance, in light of what several commentators taught on 1 Corinthians 9:27.
"Adokimos"
The word in 1Co 9:27 that is commonly translated as "disqualified" is "adokimos" (ἀδόκιμος) in the Greek (Strongs G96), and was normally used to refer to adulterated currencies, metals, soils, etc. Specifically, it was used to describe materials that, when tested for integrity, were found to be impure -- that is, "adokimos" described counterfeits.
Perseverance
The doctrine of perseverance, sometimes derisively termed "once saved, always saved," should not be taken to indicate that mere superficial participation in Christian activities -- going to church on Sunday, claiming that one "loves Jesus," etc. -- is an indicator of salvation. Passages such as Matthew 7:21-23 and Christ's words to the church of Laodicia in Revelation 3, among many others Biblical texts, indicate that not all who call themselves Christian will enter into heaven. Perseverance is granted to the members of the "invisible church" (the "wheat"), as a subset of the "visible church," which also includes the "chaff" (Mt 3:12). See John Darby's Synopsis on 1Co 9:27.
Conclusion
Several commentators have suggested that Paul was expressing concern not over his salvation, but rather over the particular reward ("crown") that he sought to obtain in heaven.1 F.B. Meyer saw the verse as indicating Paul's recognition of the fact that his ability to win souls to God was actually a result of Christ working through him, and that God could just as easily use another in Paul's place. (Cf. Lk 3:8). Gill understood "adokimos" to refer to disapproval from people, rather than rejection by God, if Paul were to live in a way that was discordant with the Gospel that he preached.
Of course, Wesley's commentary describes the verse as a direct indication that the elect may lose their salvation, which interpretation was in keeping with Wesley's Arminian theology. Adam Clarke, as a Methodist, echoed Wesley's understanding in his own commentary.
Calvin, the theologian most closely associated with the Doctrines of Grace (which includes perseverance), offers the following interpretation:

"That, when I have preached to others..." Some explain these words in this way — “Lest, after having taught others with propriety and faithfulness, I should incur the judgment of condemnation in the sight of God by a wicked life.” But it will suit better to view this expression as referring to men, in this way — “My life ought to be a kind of rule to others. Accordingly, I strive to conduct myself in such a manner, that my character and conduct may not be inconsistent with my doctrine, and that thus I may not, with great disgrace to myself, and a grievous occasion of offense to my brethren, neglect those things which I require from others.” It may also be taken in connection with a preceding statement, (1Co 9:23) in this way — “Lest I should be defrauded of the gospel, of which others are partakers through means of my labors.”  

Finally, we can remember that the passage from First Corinthians was written by the same Paul of Tarsus who wrote 1 Corinthians 1:8, Phillipians 1:6, and other passages that are widely interpreted as clearly communicating that: 1) Perseverance requires diligent effort on the part of the individual, and 2) Perseverance is a work that God, in his own strength, accomplishes in believers. That Christians' perseverance is accomplished by God is made especially clear at John 6:35-40:

Jesus said to them, “I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst. But I said to you that you have seen me and yet do not believe. All that the Father gives me will come to me, and whoever comes to me I will never cast out. For I have come down from heaven, not to do my own will but the will of him who sent me. And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day. For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”

See Scofield's Reference Notes on 1Co 9:27 and Albert Barnes' Notes. Barnes also calls on Edwards in support of the same interpretation.

A:

From the point-of-view of someone who belives in the Doctrines of Grace
The doctrine of Perseverance of Saints as defined in the link you provided

Perseverance of the saints is the Calvinist doctrine that those who
  are truly saved will persevere to the end and cannot lose their
  salvation. It doesn't mean that a person who is truly saved will never
  lose faith or backslide at any time. But that they will ultimately
  persevere in faith (inspite of failures) such as not to lose their
  salvation.

The keyword in the doctrine is perseverance, that is, those who are truly born again will not fall from God's grace and these people will show that they are truly of God by persevering unitl the end (or when Christ returns)
Regarding the verse you've showed, it's possible to view it as though Paul is striving the persevere with his walk as a Christian.
Moreover, in the same letter of Paul to the chruch of Corinth, he mentioned this in his thanksgiving:
1 Corinthians 1:4-9, ESV, emphasis mine

I give thanks to my God always for you because of the grace of God
  that was given you in Christ Jesus, that in every way you were
  enriched in him in all speech and all knowledge— even as the testimony
  about Christ was confirmed among you— so that you are not lacking in
  any gift, as you wait for the revealing of our Lord Jesus Christ, who
  will sustain you to the end, guiltless in the day of our Lord Jesus
  Christ. God is faithful, by whom you were called into the fellowship
  of his Son, Jesus Christ our Lord.

When we look into other letter of Paul, in Phil. 1:6

And I am sure of this, that he who began a good work in you will bring
  it to completion at the day of Jesus Christ.

We see in another perspective that God works graciously on Paul.
Personally I would like to term it as Perseverance of the Saints through the Preservation of God, though it's too long to be catchy!

