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-
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.