赞同曾老师的解答。我稍作补充说明。

        正如曾老师所指出的，during which引导非限制性定语从句，which为关系代词作介词宾语，先行词为时间或事件名词，定语从句对该时间或事件作补充说明。而during which time引导非限制性定语从句，which为关系限定词，限定名词time，which time作介词的宾语，先行项为整个主句。例如：

He died in 1938, during which my great-grandfather fought side by side with him against Japanese army. (during which指during 1938=when)

He died in Anti-Japanese War, during which my great-grandfather fought side by side with him. （during which指during Anti-Japanse War）

        以上两个句子中的非限制性定语从句都是修饰主句中的名词，第一句中是修饰时间名词1938，第二句中是修饰事件名词Anti-Japanese War。第一句中的先行词是时间名词，因此定语从句也可以用when引导。第二句的先行词表示事件，则不能用when引导定语从句。

The fire lasted 5 hours, during which time everything in the house was distroyed.

        (during which time=during that time=during the time of the lasting of fire)从逻辑上看，屋里的东西被烧坏是在大火持续的过程中发生，5 hours是大火持续时间的度量，而定语从句补充说明大火持续过程中发生了什么事情。因此which的先行项是the fire lasted （a certain length of time）, 而不是名词5 hours. 这种定语从句的主句中不一定有时间名词出现。例如：

He stayed in London, during which time he tried different jobs.

         (during which time=during his staying in London=during that time).which的先行项是主句的内容，which作为关系限定词修饰名词time，再做介词during的宾语，意为“在他住在伦敦这段时间里”。这句话中的which指代主句内容和上一句which的作用是一样的，区别是这一句中没有时间名词，更容易看出which指代的是主句内容。上一句中表面上看好像是定语从句修饰5 hours, 其实不是，从逻辑上分析，定语从句还是修饰主句的。这就是为什么不能用during which, 而要用during which time.

The fire lasted 5 hours, and during that time everything in the house was distroyed. 指示代词that指代主句内容。

It took two years for me to get better, during which time he spoon-fed me and did absolutely everything around the house. 

        during which time=during the time for me to get better=during my getting better=during that time. which的先行项是不定式短语for me to get better, 而不是two years. 因此定语从句不能用during which引导。

        再看一个例句：

It will rain tomorrow，in which case we will have to put off the picnic.

        in which case=in the case of the possible rain tomorrow=and in this case. 关系限定词指代主句的内容，意为“在明天要下雨这种情况下”。定语从句不能用in which引导。

It will rain tomorrow. In this case we will have to put off the pincic. 指示代词this指代主句内容。

        介词加关系代词或关系限定词which的使用范围大于关系副词when. when引导的定语从句通常都可以用介词加关系代词或关系限定词which来解释，但反之则未必。