Let’s look at three reasons that confirm that the gifts of the Spirit remain alive in the church today.

And he said unto them, Go ye into all the world, and preach the gospel to every creature.  16  He that believeth and is baptized shall be saved; but he that believeth not shall be damned. 17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues;  18 They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover.  (Mark 16:15-18)
 

In Mark 16:15-18, the command is to go into all the world and preach the gospel.  Immediately we see that this command is not just for the original apostles of the Lord since it was physically impossible for them to accomplish this commission.  Not only were they limited by the length of their earthly lives, they were limited by the lack of available transportation to reach every tribe and nation on earth.

Jesus' commission wasn't just to them, but to the entire church.  If not, then we are not called to preach the gospel today, because that commission died with the last apostle.  This is a serious point.  Are we or are we not called to reach the nations with the gospel?  Was this command only to the apostles of the Lord?  If the command is viable and active for us today, then what follows is also pertinent.

In Mark 16:16, "He that believeth" refers to those of the nations who become believers at the preaching of the gospel.

In verse 17, "These signs shall follow them that believe," is a promise to those same new believers.  The new believers of verse 16 are the same believers who have signs following them in verse 17.

What signs will follow these new believers?  They shall cast out demons, they shall speak with new tongues, they shall take up serpents (as in the case of Paul on the island, when one attached itself to him and he suffered no harm), if they drink any deadly thing, it shall not hurt them, and they shall lay hands on the sick and they shall recover.

In verse 20, the Lord was working with them confirming the Word with signs following. The Lord is still working with those who believe and still confirms the Word with signs following. 

If the preaching of the gospel is to reach all nations, then the signs that follow that preaching are still valid. And those who respond to that preaching will also have signs follow.  Logic dictates that the apostles of the Lord couldn't be around generation after generation to lay hands on each new believer.  The power wasn't the apostle's power, it is the Lord's power and confirms the gospel.  It still does.

2.  The promise of the Father (Luke 24:49, Acts 1:4) was received by the 120 on the day of Pentecost and was preached by Peter on that same day as being for "as many as the Lord our God shall call" (Acts 2:39).  This promise of power and signs is for all who call upon him.

3.  For the gifts (charisma) and calling of God are without repentance ‘ametameletos’ (irrevocable).  (Rom. 11:29)

These irrevocable, charis gifts are described in 1 Cor. 12:4-11. 

Now there are diversities of gifts (charisma), but the same Spirit.   (1 Cor. 12:4)

So, we have the witness of three.  1)The Great Commission to all nations with signs following;  2) the Promise of the Father of the Baptism of the Holy Spirit (endued with power from on high - choose your favorite term) which is for all who come to the Lord;  3) and the gifts of God which are irrevocable.

We can add to that Paul's clear statement in 1 Cor. 1:7

So that ye come behind in no gift; waiting for the coming of our Lord Jesus Christ:  (1 Cor. 1:7)

Paul’s understanding was that the gifts of the Spirit would be in operation until the coming of the Lord. We can confirm this with the famous quote of Jesus in Acts 1:8.

But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.   (Acts 1:8)

This 'promise' is the power that we need to reach the nations with the gospel of God's love. Until that commission is completed, the power is here and available to those who believe.

Jesus declared: And this gospel of the kingdom shall be preached in all the world for a witness unto all nations; and then shall the end come (Mt 24:14)  

Once this gospel is preached to all the world as a witness (Acts 1:8), then the power, the signs, the tongues, and other gifts will have fulfilled their purpose.  There will be no more need.  But as long as the Great Commission is in effect, the power, the gifts and the signs are 'irrevocable.'