How did it happen that the law that Thomas More respected did not save him when he needed it the most?
When Henry visits More to ask him for his support, More makes very clear that there is a distinction between God's law and that of the king. He also says that although he will respect the laws of King Henry, there is a part of him that he reserves for himself, and that part--his soul--belongs to God. The point is that although More respects the laws of this world, he pays greater homage to the laws of God. However, the point under contention is that More refuses to say he supports the King in his divorce; he prefers not to say anything at all, but this Henry will not let him do. And for this he dies.
The law was controlled by King Henry VIII. Despite the fact that they had a Parliament (and had had one for several centuries), Henry still controlled people with fear and money (land, titles, etc.). Henry wanted a divorce, and there weren't very many people who were willing to risk their heads to oppose him - Sir Thomas More lost his because he did oppose Henry.