Was the Apostolic Tradition of rejecting soldiers from the church ‘permanent’, or was this ‘tradition' briefly enforced? In the Bible Jesus encounters Roman soldiers but does not tell them to 'quit their day job'. Jesus encountered a centurion with 'great faith' as recorded in Matthew 8. Peter as well baptized a centurion, named Cornelius. A centurion was a higher ranking soldier over a hundred strong experienced Roman army men underneath him. (One can only imagine what a man like that would have had to go through to be honored with such a rank especially in the brutal history of Rome). After preaching and praying the Holy Spirit 'fell upon' those they were gathered among Peter and Cornelius and Peter exclaimed in surprise and excitement;


  “Surely no one can stand in the way of their being baptized with water. They have received the Holy Spirit just as we have.” So he ordered that they be baptized in the name of Jesus Christ. (NIV Acts 10:47-48).


Here we find Peter not only 'accepting the soldier', but calling for an 'immediate baptism' -- both against the 'Apostolic Tradition' handed down from Peter?!

Understandably, when Christians were on the ‘hit list’, a Christian soldier, faced with having to kill a Christian, would have had to switch sides and become a martyr.  In these same conditions, I assume that serving in the Roman army almost became synonymous with the ‘anti-Christian’ beast of Rome, so in the Apostolic Tradition, I can partly accept the rejection of soldiers from the church (actually rejection of soldiers, actors and others):


  If someone is an actor or does shows in the theater, either he shall cease or he shall be rejected. ... 11The catechumen or faithful who wants to become a soldier is to be rejected, for he has despised God. (Hippolytus, The Apostolic Tradition)


What I am wondering was, 'Is there any indication in this tradition by Hippolytus of Rome that the Church in Rome was supposed to have kept this Apostolic Tradition, or was this just a temporary measure of the church in Rome at that time?
This answer is based on the article Christians and the Roman Army AD173-337 by John Helgeland (Church History 43(2):149-163, 200; 1974). The start date of AD173 is the year when we have the first evidence (after the NT) of Christians in the military - in Legio XII Fulminata (the Lightning Legion) under Marcus Aurelius.

Prohibitions on members of the (Roman) military becoming Christian were not universally enforced, and there was disagreement among the Fathers as to whether it was possible to be Christian and a soldier at the same time. Certainly Christians should not take part in persecutions. Torture and capital punishment (for which officers were responsible) were also identified as wrong. On the other hand, the ordinary work of the army was not necessarily considered to be bad. Clement of Alexandria (Protrepticus 10) sees it as just another profession, and Tertullian in his early writings urged Christians to pray for the Empire and her armies (Apology 30):


  Without ceasing, for all our emperors we offer prayer. We pray for life prolonged; for security to the empire; for protection to the imperial house; for brave armies, a faithful senate, a virtuous people, the world at rest, whatever, as man or Cæsar, an emperor would wish. 


Origen believed (Contra Celsum 8) that while Christians should not personally serve as soldiers, they should still pray for Roman victory (in wars which were just). In this view, it's not that there's something inherently morally wrong about being a soldier - but only that it is problematic for a Christian to serve in a non-Christian army, for a non-Christian empire. 

A related problem was that Roman military service was bound up with Roman religion; Tertullian's On idolatry identified the taking of an oath to the state to be un-Christian, and moreover, Roman military standards (signa militaria) were given special reverence, placed in a sanctuary in the camp so that soldiers could pay homage - these were signs of the gods-given authority of the emperor. Origen, similarly, said that since all authority comes from God, it is not right to give this honour to Caesar. Several Christian soldiers were martyred towards the end of the third century for refusal to perform army rites, objection to the idolatrous nature of the signa militaria, etc. This was intensified under the persecution of Diocletian, who issued edicts to require all soldiers to take part in sacrifices and other rites - the intention being to get rid of Christians in the army, which implies that there must have been a substantial number of Christians there to be purged. So any prohibition on military service, on the part of Christian leaders, was not being well enforced at this time.

After the conversion of Constantine to Christianity, the force of many of these objections was removed, and subsequent authors find little difficulty in commending Christians to military service. This is the case for Lactantius and Eusebius for example, who were both very pro-Constantine and regarded him as being on a divinely-approved mission. After Constantine we find many graves of soldiers whose inscriptions record their Christian faith in addition to their military service.

In summary, Helgeland argues that the prohibitions in Hippolytus and elsewhere should not be construed as objections to military service in general, but only to the specific idolatrous and persecuting nature of the contemporary Roman army. Moreover, Christian responses differed - some said that Christians should avoid military service entirely, while others would allow it, but on the assumption that the soldier should refuse to participate in evil activities (and accept the consequences).