" For the second time" vs " For a second time"
1. Please pay careful attention what I'm saying because I will not say it for a second time (or ...say it again).
or
2. 1. Please pay careful attention what I'm saying because I will not say it for the second time (or ...say it again).
I would say 'the second time' but I`ve noticed that 'a second time" is sometimes used. Could anybody tell me when to use " for a second time" and " for the second time"?
By the way, can I leave the word " for" out in " for a second time" or " for the second time" without lossing or changing the meaning?

Question

Answer

I would leave out "for" in both these sentences. It sounds unnatural to me to include it. The correct sentence would be "Please pay careful attention to what I'm saying because I will not say it a second time."

As I understand it, "a second time" is indefinite while "the second time" is definite and refers to a specific and known "second time".

Examples:
"I went to America for the second time in my life"
"There won't be a second time"
"Will you sit the test a second time if you fail?"

Answer

“For A second time” is better is you have not yet said it twice.  You can leave out “for a.”   You would not use “for THE second time” if the second time has not happened yet.

If you are in the process of saying something again, you can say: “For the second time, I’m telling you X.”  In this usage, you cannot leave out “for the.”