Final answer:
SS-Hauptsturmführer von Linden keeps "Verity" alive in "Code Name Verity" to extract important military information from her at the Château de Bordeaux.
Step-by-step explanation:
In the book "Code Name Verity," SS-Hauptsturmführer von Linden is keeping "Verity" alive primarily to extract military information from her. Von Linden is an intelligent Nazi interrogator who understands the value of the information that Verity holds as a British spy. Therefore, the main reason for her prolonged survival under his captivity at the Château de Bordeaux is utilitarian, as he aims to gain as much intelligence as possible to aid the German war effort.