If miracles stopped after the Apostles, then why are there admonitions to pray over people?

James does not even hint that a special spiritual gift is involved, nor that a miracle would be performed. Garden variety elders are called (not someone with the gift of healing), and answers to prayer are anticipated, that's all. And that is enough. An answer to prayer need not be a miracle nor even miraculous.

The interaction between God's sovereignty and our wills and desires is a mystery, and there is comfort in knowing that the laws of physics need not be suspended every time the Lord intervenes for us, which I believe is every moment of every day.

1- We are called in 1 Thes. 5:17 to "pray without ceasing" 2- We are called in Philip. 4:6 to "but in every situation, by prayer and petition, with thanksgiving, present your requests to God." 3- In 1 Tim 5 Paul could not heal Timothy & 2 Tim 4 Paul could not heal Trophemus.

The Timothy letters were written around AD 62-66 and James around AD 62.

We don't witness healings beyond Acts 28 which was around AD 61-62. The "sign gifts" were fading away as that which is Perfect "The Completion of the New Covenant (Testament)" was nearly complete.

It is agreed by many Scholars that after this time there were only 6 more books written, Jude, Revelation, the Gospel of John and John's 3 Letters. No mention of healings or other Apostolic gifts.

We won't count the Prophecy of Revelation because the Old Covenant Prophets were given their inspired books sometimes in similar manner.

For a timeline of the Books written there are many, but here are 2- http://www.biblestudytools.com/resources/guide-to-bible-study/order-books-new-testament.html Additional Resource- http://www.compellingtruth.org/New-Testament-timeline.html

Bear in mind that when a book was written and when the actual events occurred are 2 different things.

Prayer & Faith are our weapons against sickness today and in the Lord's eyes that is sufficient, if he so chooses to heal us. The ultimate healing is our Perfect glorified bodies we will have when we are taken home.

I think this verse means to that we should pray for those people who are physically sick and in some ways I partially believe in a kind of limited cessation. You can see a very lengthy response to the state of all the gifts here Are the gifts still active?.

Although at the time this letter was written the healing may have commonly been extra ordinarily miraculous, however, just because we pray for someone that is sick does not mean that God will not answer by normal means such as bed rest, even at that time in history. Whether God answers miraculously, or just supporting the person under a time of temptation and giving him and his doctors wisdom to take the proper care, or whether God’s answer is to simply bring that person home into heaven the next day, of course prayer should be offered! So this verse does not relate directly to the question of cessation or not cessation. Whenever we are in distress we should seek prayer especially when we are truly sick.

Going to God in payer simply assumes that God could heal, or otherwise help us in our sickness. The answer to all of us, at some point in our prayers, will be comfort and strength to face a death we are peacefully prepared for.

Would we expect any Church not to encourage sick people to be prayed for?

It is important to distinguish between cessation of spiritual gifts being bestowed on individuals, and cessation of all miraculous events entirely. Cessationists consider the first case (individual bestowment of spiritual gifts) to have ceased, but not all miraculous events entirely. See B. B. Warfield's Counterfeit Miracles, in the section titled Faith Healing:

"In the healing of every disease of whatever kind," writes Doctor Henry E. Goddard, "we cannot be too deeply impressed with the Lord's part of the work. He is the operator. We are the co-operators. More and more am I impressed that every patient of mine who has ever risen up from his sick bed onto his feet again has done so by the divine power. Not I, but the Lord, has cured him. And it is this fact that the Lord does so much, that gives to different systems of healing their apparent cures. He has healed many a one in spite of medicine, in spite of mental healers, in spite of ignorance, in spite of negligence and poor and scanty food. Nineteen out of twenty cases of grippe will get well without doing anything for it, if we are willing to bear it until that time. Pneumonia, even, is what the physician calls a self-limiting disease, and many cases will recover alone if we are willing to run our chances with it. The arm may drop into boiling water and become scalded. Nine times out of ten it will take care of itself and heal. But if that arm is mine it is going to have an outward application which will make it feel better the moment it touches it. And more important by far, it is going to be dressed aseptically to prevent blood poisoning. It might get well itself, probably would; but it is going to have my little co-operation, the most intelligent that I can render, that the Lord may have the open door through which He can come in and bless it." It is the very spirit of James, I take it, that speaks in this Christian physician. If you are sick, you will use means, all the means that exist; but you will use the means in the name of the Lord, and to Him you will look for the issue. (172–173)

In short, cessationists hold that the sovereignty of God is such that all healing of any sickness is the result of God's working, and also hold to the miracle of salvation as the pre-eminent form of still-continuing miracle. Indeed, the miracles that have ceased are those apostolic-era gifts used only for the purpose of spreading the gospel in the early church; those that were bestowed on individuals, rather than purely by God's working.

In James 5:14, no individual has been bestowed with a gift of healing. Rather, with prayer foremost, and secondarily medical care in the form of anointing of oil (historically considered to have medicinal value), a group of the elders of the church were to care for the unwell individual. The hope is that God would then miraculously heal the individual. However, this is quite a different circumstance to that of the apostles and those granted the gift of healing, who could "at will" heal anyone they chose.

With that in mind, cessationists would encourage this practice (perhaps not with oil specifically, but the best available medical care), but would not consider any of the elders to have been bestowed any spiritual gift of healing in the event of a miraculous healing.

It is worth noting that John Calvin, in his commentary on James 5, considered the anointing with oil, prayer, and resulting healing to be an apostolic sacrament which has passed. This is no longer the predominant position among cessationists, to the best of my knowledge. However, even at the time he wrote, others considered the anointing with oil to be medical (a common view today as well), and thus only the prayer was efficacious, in as much as God chose to heal the sick in that instance.