I have done a lot of searching, and all I can find is that he died, not how. He seems to be one of the only kings of England that doesn't have any documents specifically on his death.
Stephen fell ill with a stomach disorder and died on October 25, 1154, at Dover Priory while traveling. He was buried at Faversham Abbey with his wife Matilda and son Eustace.
King, Edmund, King Stephen (The English Monarchs Series) Edit to add the author is a professor at the University of Sheffield.
Note: I have not read the book. I followed the wiki citations and dug around until I found a reliable source. It's currently available on Kindle for $20. Hope that helps.