In the article it is speculated the main patient didn't get better during the initial course of treatment because the bacteria infecting him resisted the multip

In the article it is speculated the main patient didn't get better during the initial course of treatment because the bacteria infecting him resisted the multiple phages they used to treat him - they were all variants of the same vector of attack(that worked in the labs on the bacteria in question), and the researchers had to find different phages to continue treatment, so they came across resistant bacteria immediately.