It's the third time I have shown you how to do it.
The main reason it is used in your sentence is this:
The actual moment in the past when this action of showing occurs is not specified or relevant to the speaker, just the fact that it is IN the past.
Compare it to: Yesterday was the third time I showed you how to do it.
In this case, it has nothing to do with repetition. It has to do with the past moment not being specified or specific. It's just past [finished]. You want to say the thing occurred in the past without specifically saying when in the past it occurred.
This non-specified use of present perfect is different from:
I have never eaten fish. [That means, until now, and up to this moment, I have not eaten fish.]