Well the Book of Acts mentions the martyrdom of the Apostle James, and the martyrdom of Stephen. It seems extremely unlikely that it would exclude the martyrdom of the two most prominent Apostles and Christians.
Yes, it is somewhat an argument from silence, but when the events are monumental, and hold directly to the two biggest “characters” in the book, it makes sense to question why it wasn’t mentioned.
I’m quoting from Sean A. Adams’
The Genre of Acts and Collected Biography (chapter 6 ‘Peter, Paul and the ending of Acts’, pp. 242-3, most footnotes omitted):
In the discussions regarding the closing of Acts mentioned above, commentators question the ending because it leaves unfinished much of the Pauline narrative. This is exemplified by [Ben] Witherington’s assertion, '‘If Acts is biography, it would seem clearly to be an unfinished work, for the audience is left suspended in midair, waiting to hear about the fate of the hero of the last half of the book.’ (159: Witherington,
Acts, 808.) This statement is interesting in that it presupposes that the conclusion of Paul’s life is foundationally important in biographical traditions. Though it is true that in individual biographies the death of the main character is one of the most important features, this is not the case for collected biographies.
Acts is not an individual biography in which all of the formal features of a life are required. Rather, the portrayal of Paul is embedded within a larger narrative and literary work in which the gospel of Jesus is the most important feature, not the individual disciples. Though the focus on Paul is an important component of the Acts narrative - particularly in light of the amount of storyline it entails - an emphasis on a single disciple is not the focus of collected succession biographies. On the contrary, the disciples are only important due to their fidelity to the message of the founder, for it is the message that is paramount.
The death of a disciple was not a requisite feature of collected biographies, and so Paul’s death could be unproblematically omitted. The omission of Paul’s death parallels that of Peter, the other main character in Acts, and further supports the idea that Luke intentionally left out this detail. The symmetry in the handling of these two characters, concluding their narrative as they are continuing their ministry, parallels the treatment of disciples in collected biographies and focuses the narrative on the teacher and his teaching.
It is possible, moreover, that Paul was becoming too large a character, and so a fully detailed trial and death would have detracted from the reader’s focus on the gospel message and would have shifted it to the person of Paul. Furthermore, Acts is not a martyrology of Paul and does not require his death: ‘[Luke] did not see it as his task to enhance devotion to the martyrs’. (162: Haenchen,
Acts of the Apostles, 732.) Paul, in being a faithful minister and preacher, had already done his important work by bringing the gospel to the gentiles. True, Paul’s appearance before Caesar (if it happened at all) would have been interesting, even inspiring, but it would have possible risked creating too many parallels between Paul and Jesus. In fact there is a strong possibility that Paul’s trial in Rome before Caesar might have overshadowed that of Jesus, who was only judged by a minor administrator in a troubled province. Further, as there would not have been the miraculous resurrection for Paul than there was for Jesus, the conclusion of Acts would have presented a vastly different feeling and perspective of the early church and thus a different message to its readers.