Excerpts and ideas from:
Cessationism vs Biblicism 1
Cessationism vs Biblicism 2
Cessationism vs Biblicism 3

The following is taken from:
Cessationism vs Biblicism 1

IS CESSATIONISM BIBLICAL?
Here we must once more emphasise the fact that there are degrees of cessationism - see the examples above. To say, as was common among a number of branches of conservative evangelicals several decades ago, that supernaturalism ended with the passing of the original apostles is without any biblical support. Statements such as, "Jesus Christ the same yesterday, and to day, and forever" (Hebrews 13:8), whether interpreted solely in relation to the context or taken as a great principle of the gospel, clearly denies the idea. There are many biblical statements that teach the same thing.

"For I am the LORD, I do not change; therefore you sons of Jacob are not consumed" (Malachi 3:6).

"Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom is no variableness, neither shadow of turning" (James 1:17).

What we are discussing here is what theologians call the immutability of God. The extreme cessationist view is so clearly contrary to the doctrine of the changelessness of God as taught in scripture that we would only labour the point if we quoted more passages from the bible against it.

The more moderate view is not so easily dismissed as it impinges upon another equally important theological truth, which we call the sovereignty of God and which needs to be held in tension with God's immutability. Cessationists tend to focus on the former whereas most Pentecostals and charismatics focus on the latter. Correct teaching about each will not deny or undermine either. This is where the art of rightly dividing the Word of Truth by comparing scripture with scripture, is so important. Sovereignty says that God can choose to withdraw the displays of His supernatural powers. Immutability says that He will only do so in accordance with His nature and character as revealed in His Word, the bible.

Far from sovereignty denying and undermining immutability, the fact that God is SOVEREIGN means that He is able to maintain the changelessness of His ways and works. Now this is the principal part of the premise on which we must build our argument in respect of our topic.

Cessationism affirms that God in His sovereignty has determined to cause certain things that He gave to the early New Testament church to cease or come to an end. We say that such a position must not be arrived at arbitrarily by conjecture, nor simply on the basis of history as we perceive it, but by scripture. Does the Word of God establish (prove) it?

To those in the Pentecostal and charismatic camps we would issue the same challenge. Let the Word of God decide and let history and experience illustrate what the bible teaches. To the one we say, "Take out your bibles and show us clearly where scripture teaches that the supernatural displays of God, including the nine gifts of the Holy Spirit and the five ascension ministry gifts of Christ, are said or prophesied to cease and we will support your view. Do this before you make your appeal to church history."

To the other we say, "Take out your bibles and show us clearly where your strange and sometimes bizarre so called manifestations of the Holy Spirit find support. Do this in a reasonable and convincing manner before appealing to experience or history and we will go along with you".

I believe there are 2 things in balance or tension. They are God's Sovereignty vs God's Immutabilty.

This tension is not easy to understand. If you claim all supernatural gifts have ceased -- you are denying God's Immutability. If you claim that a person with the gift of healing should be able to heal at will 100% of the time you are denying God's Sovereignty.