“Let us not hesitate to help those who have died and to offer our prayers for them.” —St. John Chrysostom
All four raised the dead, and prayed for them before they were raised; therefore, they prayed for the dead, and it is recorded in Scripture. It’s inescapable logic:
1) Elijah: 1 Kings 17:17-24 (17:21: “Then he stretched himself upon the child three times, and cried to the LORD, “O LORD my God, let this child’s soul come into him again.”).
2) Elisha: 2 Kings 4:18-37 (4:33: “So he went in and shut the door upon the two of them, and prayed to the LORD.”).
3) Jesus: raising of Lazarus: John 11:41-42 (11:41: “Father, I thank thee that thou hast heard me.”).
4) St. Peter: raising of Tabitha: Acts 9:36-41 (9:40: “Peter put them all outside and knelt down and prayed.”)
In all these instances, a prayer for the dead person is recorded (Elijah’s being the most specific and undeniable). Jesus also “prayed” (or at least talked) to the dead, when He cried, “Lazarus, come out” (Jn 11:43), and to the dead son of the widow of Nain: “Young man, I say to you, arise” (Lk 7:14). St. Peter did the same, saying, “Tabitha, rise” (Acts 9:40).
This was invocation of (or, in a very loose sense, “prayer to”) the dead, insofar as they talked to a dead man. Thus, if someone claims this “never” happens in the Bible, or that it has no scriptural warrant, they are wrong.
St. Paul also prayed for the dead man Onesiphorus (2 Timothy 1:16-18).
They may say, “well, that is a special case, when someone is being raised from the dead.” It is a special case, granted, but these are nevertheless cases of praying for the dead. It can’t be denied.
Prayer for the dead is even more explicit in 2 Maccabees 12:42, 45: a portion of Scripture that Protestants have thrown out on inadequate grounds:
2 Maccabees 12:42, 45 and they turned to prayer, beseeching that the sin which had been committed might be wholly blotted out. And the noble Judas exhorted the people to keep themselves free from sin, for they had seen with their own eyes what had happened because of the sin of those who had fallen. . . .  For if he were not expecting that those who had fallen would rise again, it would have been superfluous and foolish to pray for the dead.  . . . he made atonement for the dead, that they might be delivered from their sin.
This passage describes the practice of prayers for the dead: the basic practice. It was practiced by the Jews and wasn't condemned in the text; therefore God approved of it. This is of the utmost significance. If it were wrong, the text would have indicated that, and it would be significant: if not as Scripture, then as historical reference to what the Jews believed was right or wrong practice. But Maccabees is Scripture; therefore inspired and infallible. It was thrown out on inadequate grounds.
1 Corinthians 15:29: “baptized on behalf of the dead” is also relevant. It means, I think, “doing penance on behalf of the dead”: according to the exegesis of St. Francis de Sales, and taking into account the striking similarity to 2 Maccabees 12:44.
What I'm contending is that this eliminates the absolute prohibition among some Protestants of either prayers for the dead, or invocation of the saints, or any communication whatsoever with the dead. If Jesus and Peter talked to dead men, then obviously there is a proper sense in which that can and should be done.
The argument above doesn't claim address the issue comprehensively, but rather, in a limited aspect: dealing with a key hostile premise. Let me further explain:
1) A belief that no communication whatsoever between the dead and the living is permitted (and that all of that is identical to forbidden necromancy, seances, etc.) obviously precludes from the outset prayers for the dead and invocation of the dead: asking for their prayers.
2) A belief that such things are not seen in the Bible at all would preclude their practice for Protestants, who think that every doctrine or practice must have express or explicit biblical sanction, and (in large part) for Catholics, most of whom who believe that all Catholic doctrines have at least some biblical evidence in their favor, or that they are at least harmonious with what is in Scripture.
3) The above examples simultaneously take out #1 and #2 as objections.
4) Therefore, a root premise of the communion of saints is established as true and permissible (biblically).
5) #4 is an altogether worthy and useful end.
6) Therefore, these biblical arguments are helpful aids in both apologetics towards non-Catholics and an aid to confidence among Catholics: who are so often accused of being “unbiblical” or “anti-biblical.”
It's always good to appeal to the Bible as much as possible. That's not just a Protestant thing. The apostles and fathers did it all the time. There is no necessity of accepting sola Scriptura in order to massively cite the Bible. That is another fallacy. Protestants don't “own” the Bible. I don't become a Protestant in my essential methodology simply because I cite the Bible a lot. All the Church fathers did the same thing.
Lastly, prayer for the dead is not at all unknown in Protestant circles. Luther acknowledged a minimalistic sense of it. Lutheran confessions include it (and they practice it); same with Anglicanism. I was at an Anglican funeral service for my grandmother, where the priest prayed for her.
Among the Reformed and Baptists, it's a different story (as so often). But that's not the whole of Protestantism, by any means. Thus, to say that “Protestants as a whole reject it” is untrue. Two of the initial forms of Protestantism continued to accept it as a valid practice. And they must do so (presumably) for some reason.
The Protestants who decided to become less sacramental, sacerdotal and traditional (with no legitimate basis) rejected it.