▲这个 to 不能省略，因为这个 reply 是不及物动词，此处的搭配是 reply to my letters（回复我的信）。你的句子意思是“我写的信没有一封得到回复”。又如：

I was late in sending my reply to his letter. 我给他回信晚了。

I am puzzled by his failure to reply to my letter. 他不给我回信使我百思不解。

Despite wanting to see him again, she refused to reply to his letters. 她尽管很想再见到他，但却不愿给他回信。

Their failure to reply to our letter seems to imply a lack of interest. 他们对我们的信件不予答复似乎暗示不感兴趣。

▲注意：你查词典可能查到 reply 也可以用作及物动词，但是注意，reply 用作及物动词时，它不能接名词或代词作宾语，而只能接从句作宾语。如：

He replied that it was out of the question. 他回答说那是不可能的。

She replied that she couldn’t come. 她答复说，她不能来了。

He replied that he didn’t like it. 他回答说他不喜欢它。

He replied that he knew nothing about it. 他回答说关于这件事他什么也不知道。 

▲英语语法网的以下文章可以参考一下：

http://www.yygrammar.com/Article/201102/1966.html