The Anti-Life worked for one simple reason; The Anti-Life was stronger. This was proven by the Greek Gods being ousted, and having their lasso and other powers fail them. I think Anti-Life didn't so much as make Diana a slave and a masochist against herself, but changed the reality of who she was, on a higher level then she had been created on.
Anti-Life was, and with the exception of a very very crappy mini we will not speak of, has always been sold as the almost the source code of will and existence. In Final Crisis Darkseid just was, if you will. It wasn't until Darkseid, that source of the new reality, was physically killed by Batman and wiped away by Superman and his machine that the lasso could star to restore the original truth, because Darkseid had created a new one. One that treated Diana in not the best way.