仔细找了一会儿,个人觉得这个答案应该可以满足你.
回答：《张道真英语用法》（商务印书馆）中关于matter有这样的例句：
the matter 表示“有问题”、“有毛病”
例句：Is anything the matter?
　　　What's the matter with the machine?
　　　What's the matter with your foot?
　　从第一句可以看出,anything是主语,the matter 是表语,那么肯定句可以是Something is the matter.或 Nothing is the matter.如果对Nothing 或 something划线提问的话,那么就是What is the matter?也就是说the matter 是表语；what 是主语,这本身就是陈述语序了.那么在直接引语转间接引语后,She asked what was the matter.是正确的.
　　但是,有可能这种语序读起来比较拗口,所以也会有She asked me what the matter was的句子出现,应该也不算错.可能2006年吧,重庆市中考题中就出现了what the matter was的正确选项,所以这种说法应该是已经被大家所接受了吧.
但从严格的语法意义上来讲,She asked me what was the matter 是正确的.
引用一位美国老师的话,可能从日常用法上说明一下：
　　Could you tell me what the matter was?is the more normal version,but I can't really say why:it's mainly a question of rhythm,I think:it sounds a little better.