One thing proponents of the Argument from Martyrdom keeps forgetting is that they not only need to show that the apostles were martyred for their beliefs, but also that they were martyred after having been put into a position where recanting would have saved them.

For example, it's not enough to show that an apostle was killed by an angry mob or even the legal authorities for what he was preaching. That doesn't show anything about the truth of his claims, one way or the other.

Instead, one would have to show that the apostle knew or claimed to know Jesus, knew or claimed to know about the resurrection, that he was threatened with death for what he was preaching, AND that, had he recanted, he would have been spared.

Do we have any examples of that happening to anybody who claimed to know Jesus and had witnessed the resurrection? Heck, do we have records of anybody in the first or second century Roman Empire being hauled before the authorities for teaching or preaching something and then being told they would be let go if they renounced their beliefs? Not just being told they would be let off with a warning if they promised to stop, but actually set free after publicly renouncing what they had said before?