--------- in a seemingly endless war,the general was forced

答案：C.Having lost over 50,000 soldiers
Having lost over 50,000 soldiers in a seemingly endless war,the general was forced to evaluate the situation again.
一、句子分析
* 主要成分：the general was forced to evaluate the situation again.
将军不得不重新估计形势.
* 原因状语：Having lost over 50,000 soldiers in a seemingly endless war 由于在一次仿佛无休止的战争中已经损失了50,000 士兵.
二、选项分析
A.Since the loss of 50,000 soldiers
since 引导原因状语从句,但是此处没有谓语动词,句子不完整.
B.Because of 50,000 soldiers having lost
Because of 是介词,尽管后面跟的宾语是动名词的复合结构,但是 having lost 是主动完成形式,不是“士兵失去”,而应该是“士兵被失去”,用被动形式 having been lost 才正确.该选项语法不正确.
C.Having lost over 50,000 soldiers
这里是现在分词短语作原因状语,逻辑主语是 the general,与分词是主谓关系,即“由于将军已经失去...”,语法正确.
D.50,000 soldiers were lost
这是一个独立的分句,与后面的句子是并列关系,语法不正确.