I do believe that love can often heal, but I do not believe that love can always cure. There have been cases of persons who are so damaged that despite being loved by others, they cannot seem to function normally in society or submit completely to healthy relationships.
Take serial killers for example. Yes, some came from hideously abusive backgrounds, but others had parents who loved them. Some had spouses or girlfriends and children that loved them unconditionally. Despite these healthy relationships, the killers were too psychologically ill to feel love and accept it as a means of healing.
I feel like I am throwing a huge wet blanket over the romantic notion of love as a cure-all, but there are too many cases throughout history which prove that it is not, which is quite tragic.