Fallible apostles exist and are gifted men of God. Many church planters, for example, may have the gifts of an apostle but they do not have authority over others even while they may have much influence. This is because whereas the gift of the apostle continues the office does not.
Sometimes cessationists make the argument that all continuationists believe that at least the gift of the apostle has ceased. I disagree with that caricature; I believe the office of Apostle has ceased. There were other apostles in the New Testament, apparently, they were gifted, and that type of apostle is still around. Obviously, no one else fits the requirement of an Apostle and thus no one should hold the office of an Apostle but that does not, therefore, mean that there are none with the grace gift of an apostle.
As we saw above, MacArthur has tried to show that the rule of apostle has ceased and so then that means that the gifts have ceased. MacArthur does not, however, succeed at what he set out to accomplish. After all, Stephan, for example, was not an Apostle and yet he performed great signs and wonders (Acts 6:8 and perhaps Timothy cf. 1 Tim 4:14; 2 Tim 1:6; 1 Thess 5:19-23; cf. Acts 8:6–7; 9:17–19; 10:44–46; 11:27-30; 19:6–7; 21:9-11). So even if there are no more Apostles that does not mean that there are not still miraculous gifts. However, I do believe there are still apostles (I am not referring to the capital “A” Apostles here, I do believe they have ceased. No one today can meet their qualifications).
But, the role of apostle still continues. Ephesians tells us that Jesus “gave the apostles, the prophets, the evangelists, the shepherds and teachers, to equip the saints for the work of ministry, for building up the body of Christ, until we all attain to the unity of the faith and of the knowledge of the Son of God, to mature manhood, to the measure of the stature of the fullness of Christ” (Eph 4:11-13). We have these five types of leaders (i.e. apostles, prophets, evangelists, shepherds, and teachers) for how long? Paul says, essentially, until perfection (this sounds similar to 1 Cor 13:10), until “the fullness of Christ.” Further, there is no reason to think that we get to keep three of the five types of leaders and lose two (i.e. the apostles and prophets).
When we take these verses into consideration, there is no reason to think that just because the Apostles were the foundation of the church (Eph 2:20) that that means that there are no longer those today that can at times, according to the will of God, perform miraculous signs. Regarding Ephesians 4, Markus Barth rightly points out that it “does not contain the faintest hint that the charismatic character of all church ministries was restricted to a certain history and was later to die out.” In fact, he says, “Ephesians distinctly presupposes that living apostles and prophets are essential to the church’s life.”