(1)It is the third time that I've explained the problem to you.

说话时第三次解释已经发生过了。句子的逻辑意义等于我已经给你解释三次了。第几次是从过去算到现在，所以与过去有关的现在要用现在完成时。

(2)It is a long time since I saw Tom at my uncle's.

主句的It is=It has been. 指从过去算到现在多长时间了。

(3)It was fifteen years since she had left home. Her home village had greatly changed.

主句为一般过去时，从更早的过去算到随后的一个过去时间有多久了。更早的过去要用过去完成时。家乡的变化在主句时间之前，所以也要用过去完成时。

第三句改为下句也是正确的。

It had been fifteen years since she left home. since的词义决定了主从句谓语时间的先后，所以从句用一般过去时代替过去完成时。