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Why do we use the present perfect with This is the first time, but the present simple/continuous with This is the last time, i.e.
This is the first time I have done it.
vs.
This is the last time I do/am doing it.
In both sentences, I see a connection from past to present and using the present perfect makes sense.
This is the first time I've done it.
One of the many uses of the perfect tenses is to talk about life experiences, which is why it is used here: talking about the first time doing it, the importance is placed on whether or not we have that experience, not what is happening. One might say, "The first time I did it..." but this would focus more on the events rather than it as an experience. Similarly, you could say, "the second time" or "the third time" still focusing on the experience aspect (but this is less common since usually only the first time is important). As to why it's not "I'm doing it" or "I do it" instead of "I've done it", it's that it loses the sense of experience that the perfect conveys.
This is the last time I do/am doing it.
This sentence is not focusing on it as an experience, but rather would usually be said if someone is agreeing to something or is doing something that they do not want to do ever again. It is important not to use this in the any sense of the past because last in the past usually conveys the sense of most recent rather than final, so it means something completely different. It is furthermore important not to use the perfect with this because this is a specific time mentioned, so there is no reason to use the perfect. (This could also be "will do", "am going to do", "will be doing", or "am going to be doing" if the speaker has not yet done the action.)
This is the first time I have done it -is possible.
Think that you fixed a door at 10 am. On 10:01 or so, you can say the above mentioned sentence. You recently, just recently, fixed the door.
Now,
This is the last time I do/am doing it -is also possible.
It's more appropriate if you are just to do something, and you have made your mind that it is for the very last time you are doing it.
In the same example, imagine that every time you fix a door, you get hurt. You don't like fixing the door anymore. But still, doing someone the favor for the last time, you may say...
This is the last time I am doing it (-don't ask me for this favor anymore).
Often, when someone says "it's the last time" (or, more commonly "this is the last time") they are talking about an act they haven't done yet. The sense is "well, I'll do it this time, but never again. So "last time I'm doing this" is actually future, like "I'm going to the movie tomorrow."
By the way, a native speaker would not say "this is the last time I DO this."
They might say "This is the last time I WILL do this" or This WILL BE the last time I do this" (and there's a Rolling Stones song that uses the phrasing "this could be the last time")
http://www.lyricsfreak.com/r/rolling+stones/the+last+time_20117882.html
