How do Pentecostals theologically justifiy when "faithful" snake handlers die? What does it mean to Pentecostal churches whose pastor dies from a snake bite?  The faith in snake handling comes from the literal interpretation of:

Mark 16:17-18 KJV


  And these signs shall follow them that believe; In my name shall they
  cast out devils; they shall speak with new tongues;
  
  They shall take up serpents; and if they drink any deadly thing, it
  shall not hurt them; they shall lay hands on the sick, and they shall
  recover.


However, on occasion, a pastor dies from a snake bite.  How does this specific segment of the denomination rationalize the death?
You ask about a specific segment of the denomination. You are confusing the Pentecostal movement (a loose description of churches that believe some similar things about the Holy Spirit and spiritual gifts) with a denomination (such as the United Pentecostal Church International, which is a denomination within the movement).

The churches that practice snake handling are (as many Pentecostal churches are) non-denominational, only recognizing the authority of the local church. They may fellowship with like-minded churches, but there is no denominational hierarchy to issue official policy or doctrine. 

So for any death caused by a snake-bite, the local pastor would likely offer the interpretation as to why God allowed or caused it. This article gives one interpretation:


  When someone does dies of snake bite, it means that he or she must not have been "anointed" by the spirit to do so. Handlers don’t believe that you should just go around picking up poisonous snakes any old time.


But the original article you linked to in your question has an alternate answer from the son of the pastor:


  when it's your time to go, it's just your time to go


In another article the same son expounded briefly:


  His father's death, he says, was "God's way" of taking him home, and his family will embrace the deadly rattlesnake that delivered his death sentence at the Full Gospel Tabernacle in Jesus Name church in Middlesboro again this Saturday.
  
  "It was God saying, this is how you wanted it, and it's your time to go. ... If he didn't plan [to die this way] he would have stayed alive," Cody reportedly told TMZ.


Here is another example of a son explaining his father's death from handling serpents. In this case, the article is about the death of the son (Mack Wolford, died in 2012 after being bitten by a Timber Rattler during a service) but in the article, he describes his own father's death from a serpent bite.


  Wolford was 15 when he saw his father die at age 39 of a rattlesnake bite in almost exactly the same circumstances.
  
  “He lived 10 1/2 hours,” Wolford told The Washington Post last fall.
  “When he got bit, he said he wanted to die in the church. Three hours
  after he was bitten, his kidneys shut down. After a while, your heart
  stops. I hated to see him go, but he died for what he believed in.”


One thing you must remember is that for any Christian, death is not viewed as the end, but the beginning of eternal life. The word martyr means witness. So in the eyes of this man's church, his death may not be seen as a bad thing, but that he died while bearing witness to his faith. (After all, Jesus, the Apostles, and many early church fathers died martyr's deaths.)

But due to the lack of structure within the movement, an official policy or statement is unlikely to be found.