that在定语从句中什么状况下可以省略除了关系词在从句中作宾语的情况,这个我已经知道了The reason (that) he did not attend the meeting was that he was ill 这句话为什么能省略

只有一种。就是你说的

这句句子不对吧 应该是 The reason why he didi not attend the meeting was that he was ill.

You can work out this problem (in) this way.Let me explain it (in) another way.表示行为方式的way前面的介词in美国人口语习惯上省略.所以说this way名词短语作宾语但相当于作状语而不是通过介词短语作状语.所以说引导way的关系词可以是关系副词where(实际上不用)也可以是关系代词that但不用which,或用in which当然也可以省略.例如：I don't like the way (that/in whinch）he speakes to his mother.
the reason和the way一样只不过省略for,但可以用关系副词why来引导.这都是美国人的习惯问题,没有为什么,可以在网上搜关于省略句的文章.

老兄，那个that 引导的不是定于从句，而是一个同位语，he did not attend the meeting 是reason的同位语。后面的that引导的是表语从句。
至于that 引导定于从句时的省略，应该是在that在从句中做宾语的时候可以省略。例如：
That is the man （that) I talked with yesterday.