What are the biblical arguments against soul sleep? Quoting from this site:


  Soul sleep is the teaching that when a person dies that his soul "sleeps" until the time of the future resurrection. In this condition, the person is not aware or conscious.


What are the biblical arguments against soul sleep?
The Bible never described someone else's soul sleeping only to be awaken at the last judgment.

Rather, what the Bible records show is that in the New Testament all of God's people who are in the state of death are away from the body and present with the Lord. They are not sleeping but are at home with the Lord.


  Yes, we are of good courage, and we would rather be away from the
  body and at home with the Lord
  
  2 Corinthians 5:8 (ESV)


Paul himself expressed, not the desire to sleep, but to be with Christ.


  21 For to me to live is Christ, and to die is gain. 22 If I am to live
  in the flesh, that means fruitful labor for me. Yet which I shall
  choose I cannot tell. 23 I am hard pressed between the two. My
  desire is to depart and be with Christ, for that is far better. 24 But
  to remain in the flesh is more necessary on your account.
  
  Philippians 1:21-24 (ESV)


2 Corinthians 12:2-3 bolsters this interpretation:


  2 I know a man in Christ who fourteen years ago was caught up to the
  third heaven—whether in the body or out of the body I do not know,
  God knows. 3 And I know that this man was caught up into
  paradise—whether in the body or out of the body I do not know, God
  knows—
  
  2 Corinthians 12:2-3 (ESV)


God knows that a man can be with Him in the paradise. This is not sleep but a relationship! Take note that The thief on the cross didn’t sleep! Jesus promised him on that day that he will be with him in the paradise! (Luke 23:43).

What all this shows is that human death is not about "cessation of existence." Rather, it is about separation.


  For as the body apart from the spirit is dead, so also faith apart
   works is dead.
  
  James 2:26 (ESV)


James 2:26 says that death is a separation of body and spirit. Both do not undergo annihilation after death. Rather, both merely separated. 

This one scripture powerfully attests the doctrine of "souls don't sleep":


  who died for us so that whether we are awake or asleep we might live
  with him.
  
  1 Thessalonians 5:10 (ESV)


Conclusion

We have cogently proven from the Bible that "soul sleep" teaching is unbiblical. The New Testament consistently shows us that souls do not sleep and that the metaphor 'sleep' used for those who are dead is merely a reference to their physical bodies appearing as if sleeping.

References:

http://www.gotquestions.org/absent-from-the-body.htm

https://carm.org/soul-sleep