Are All Christians Overcomers?

When I was first saved, I was led to believe that all Christians are overcomers, but I have come to learn that Scripture does not support this.   

To the church in Ephesus, Jesus said:

He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the tree of life, which is in the midst of the paradise of God.  (Revelation 2:7)

To the church in Smyrna, Jesus said:

He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.  (Revelation 2:11)

To the church in Pergamos, Jesus said:

He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the hidden manna, and will give him a white stone, and in the stone a new name written, which no man knoweth saving he that receiveth it. (Revelation 2:17)

To the church in Thyatira, Jesus said:

And he that overcometh, and keepeth my works unto the end, to him will I give power over the nations:  (Revelation 2:26)

To the church in Sardis, Jesus said:

He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels.  (Revelation 3:5)

To the church in Philadelphia, Jesus said:

Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is new Jerusalem, which cometh down out of heaven from my God: and I will write upon him my new name.  (Revelation 3:12)

To the church of the Laodiceans, Jesus said:

To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne.  (Revelation 3:21)

Jesus was talking to believers in each of these seven churches.  So clearly, not all believers will be overcomers.  

Paul writes in 2 Timothy 4:7-8:

I have fought a good fight, I have finished my course, I have kept the faith: Henceforth there is laid up for me a crown of righteousness, which the Lord, the righteous judge, shall give me at that day: and not to me only, but unto all them also that love his appearing. 

Believers who are overcomers will receive their reward when they stand before the Lord at the Judgment Seat of Christ.  Believers who are not overcomers will receive the free gift of eternal life, but they will not receive any rewards.

When I look around at what is happening in our world, I believe that there is not much time left to run this race.  I must ask myself: Have I fought the good fight?  Have I kept the faith?