Abdel Aziz Mohamed Albaz is quite famous in the muslim world. He is the owner of the http://www.benbaz.info/
I find stupid that this guy continued to write his blog, while staying in Kuwait. It looks like he seeks martyrdoom or celebrity. He is basically one suicidal attention seeker.
The problem is that the Kuwaiti law is clear, he can declare repentance :
If the offender declares repentance, they will receive jail terms of no more than five years or pay a fine that does not exceed 10,000 dinars ($36,000).
Luckily there is no death penality for blasphemy in Kuwait yet. The parliament voted to add one death penality amendment in 2012, but it was later rejected by the Emir. His decision was later cancelled by two-third of the parliament last month ...
The bill will only effective after the government accepts it, the Emir signs it and it is published in the official gazette within one month (end of january). So there is currently no death penality.
In my personal opinion, this arrest is simply the result of the growing conflict between the parliament ruled by Islamists and the Emir who is still quite secular (in comparision to his neighbours). The Islamists probably jailed Ben Baz to pressure the Emir in order to make him sign the law.
You must know that most people jailed due to this law got suspended sentences or were simply acquitted. I can see any real risks for him.
You have also to think about the conflict between Shia and Sunni in the Emirate and about the current neighbourhood to understand the situation. Look also at the Egypt-Kuwait relations which are quite bad.