Just read through these two conflicting views.
scribd.com/doc/2210333/Jesus … gn-Forever
and
city-data.com/forum/christia … rever.html
So which is it?
clever question. I believe He will reign forever, but not because people have incorrectly translated olam & aionios as forever.
Unfortunately, I reckon most people would be put off before reading to the end of the first article, even tho he goes on to make some good points. I disagree with him that once everything is subdued He no longer needs to reign. Kings still reign during peaceful times, actually often those times are called the “golden years” 
I believe the strongest text in support of Christ’s reign being endless is Luke 1:33: “And he will reign over the house of Jacob forever (for the ages), and of his kingdom there will be no end.” I think there are a couple ways of understanding this verse that are consistent with what Paul reveals in 1 Cor 15:22-28. Gabriel may have had Isaiah 9:7 in view: “Of the increase of his government and of peace there will be no end.” Understood in light of this verse, the sense in which Christ’s reign is endless (assuming Christ’s “reign over the house of Jacob” and his “kingdom” are to be understood as equivalent in meaning) is that the prosperity and peace which his reign is to bring about will never end. Another possibility is that Gabriel was alluding to Daniel 2:44. In light of this verse we may interpret “there will be no end” to mean that Christ’s kingdom “will never be destroyed, nor left to another people.” This would be true of the kingdom over which Christ presently reigns even if Christ is to one day cease to reign over it and (in the words of Paul) “delivers the kingdom to God the Father.”
I haven’t read the articles, but for years I have understood the following passage to imply that Christ will reign only until He has put all His enemies under His feet.
Why would Paul have written that little word “until” in the first sentence if His reign was going to last forever?
When all things have been put under Christ in His reign, then He subjects Himself to the Father that God may be all in all. This sounds as if the everlasting Kingdom will then be turned over to God so that God will reign in it from then on.
That seems fitting since it is “the Kingdom of God.”