How interchangeable are PhD students to most professors? Do most professors value their PhD students, or do they see them as easily replaceable by fresh, new blood?  If a PhD student stops working, will the professor try to fix things, or replace him like a cog in his machine?
Most PhD advisors invest a great deal of time, money, and effort in their PhD students. This is a sunk cost.

If the advisor acts as a selfish rational decision maker, he/she would evaluate the prospective (future) costs of continuing to work with the student, the likelihood of the student becoming productive again given some level of intervention on the part of the advisor, and the benefit to the advisor if the student becomes productive again. Other contributing factors may include the cost to the advisor's reputation of having a failed PhD student and the impact of a failed PhD student on the advisor's promotion prospects.

Based on these parameters, a selfish rational player could evaluate whether it is in his/her own best interests to try and "fix things" or whether to cut his/her losses and "replace him like a cog in his machine." 

In other words, there is no single action taken by "most" advisors here - the best response of even a purely selfish advisor depends on the parameters of the situation.

Finally, most of the PhD advisors I personally know also feel some level of affection for their students and personal interest in their future, and would not necessarily make the strictly selfish decision described above. Rather, most PhD advisors I know would make an irrational decision that would consider the students' interests in addition to his/her own selfish interests. Depending on the situation, it may or may not be in the student's interests to be "fixed."