Most cessations would agree that God can work miracles of healing today. The real question is "Has God authenticated anyone's ministry by miracles, signs or wonders since the days of the Apostles"? Cessationists would say "No, except the miracle of God bringing others to the new birth by his/her instrumentality".
As Rhetorician has said, it is the greater work of bringing souls to salvation. Just before Christ died, after His ministry of, debatably, three and a half years, there were about one hundred and twenty believers (Acts 1:15) in Jerusalem, and some elsewhere (eg at Sychar in Samaria). When Peter preached at Pentecost, on the first day of receiving the Holy Spirit, about three thousand souls were added to their number (Acts 2:41).
That is the greater works.
The miraculous healings of the New Testament era, apart from those of our Lord, were done only by the Apostles and by two of their close band.. Stephen and Phillip. The only other miraculous healing was by the restoration of sight to Paul by Ananias (Acts 9:17). That's it. Notice the following verses:-
Then fear came upon every soul, and many wonders and signs were done through the apostles. (Acts 2:43)
And through the hands of the apostles many signs and wonders were done among the people. And they were all with one accord in Solomon’s Porch. (Acts 5:12)
Truly the signs of an apostle were accomplished among you with all perseverance, in signs and wonders and mighty deeds. (2 Corinthians 12:12).
They were the signs of an Apostle, not of all believers, or many believers.
how shall we escape if we neglect so great a salvation, which at the first began to be spoken by the Lord, and was confirmed to us by those who heard him, God also bearing witness both with signs and wonders, with various miracles, and gifts of the Holy Spirit, according to His own will? (Hebrews 2:3-4)
And if the Church/local church was going to have ministries gifted to work miracles of healing ever after the apostolic era (eg beyond, say, AD 60) then we should expect to see the ministry named in the following verse:
And He Himself gave some to be apostles, some prophets, some evangelists, and some pastors and teachers, for the equipping of the saints for the work of ministry, for the edifying of the body of Christ (Ephesians 4:11-12).
We do not find in this verse "he gave some to be healers, and some to be workers of miracles, etc".
And then we discover Paul through whom God was healing and even raising people from the dead at an earlier stage (Acts 19:11-12 - according to historical records Gallio became Proconsul of Achaia in AD 52, cf Acts 18:12, so Paul's handkerchiefs being sent to heal people was about AD 54 or 55) lost the power to heal
(1) Timothy, advising take a little wine for the sake of your frequent illnesses (1 Timothy 5:23)... and
(2) Trophimus: Trophimus I left in Miletus sick (2 Timothy 4:20).... and
(3) Epaphroditus: Yet I considered it necessary to send to you Epaphroditus, my brother, fellow worker, and fellow soldier, but your messenger and the one who ministered to my need; since he was longing for you all, and was distressed because you had heard that he was sick. (Phil 2:24-26)
[Some claim that believers should never die of sickness claiming that if someone is not healed it is because they do not have enough faith. But did Elisha not have enough faith? - "Elisha was fallen sick, of the sickness whereof he died" (2 Kings 13:14).]
In one of his messages on Youtube Pastor Justin Peters records six faith healers who taught that believers need never fall ill, who have since died of ill health.
Finally according to James the Lord's brother, when a believer falls sick they are not to call for a worker of miracles or a wonder worker, they are to call for the ordinarily appointed elders of the church who are chosen on the basis of their spirituality (1 Timothy 3:1-7). These are the ones to call:
Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven. (James 5:14-15)
Cessationists believe that the greater works means effective preaching of the Gospel with the aid of the Holy Spirit; the continuing works of miraculous gifts and healings is a myth. This does not mean that miracles and healings no longer happen. When people get saved that is a very greatest of miracles. But cessationists believe that God worked miracles through the Apostles and a very few others to authenticate their ministry and message. Today a man's ministry can be authenticated by comparing what they teach with the completed Bible. Therefore, there is no good reason why God would give the gift of signs and wonders to any man or woman today.
The sign miracles were the work of the apostles and a few of their band only. And only those who were eye witnesses of the resurrection could be an Apostle (Acts 1:21-26) who are by their writings along with the Old Testament prophets the foundation of the church (Ephesians 2:20).
And the Word of God explicitly tells us that the last of the Apostles was the Apostle Paul:
After that He was seen by James, then by all the apostles. Then last of all He was seen by me also, as by one born out of due time. For I am the least of the apostles, who am not worthy to be called an apostle, because I persecuted the church of God. (1 Corinthians 15:7-9)
There are no more Apostles, nor Prophets, nor the signs of Apostles (2 Cor 12:12) which were given to authenticate their message of the Gospel.
[[I have used mostly "Proving the Charismatic gifts have ceased" by Dr Peter Masters, a 50 pence booklet from the Tabernacle Bookshop, Metropolitan Tabernacle, Elephant & Castle, London. Tel: UK 0207 735 7076. But buy it to see if I have said things which the author would not agree with.]]