I would use "I'll ask you again" if I was going to ask person the same question after some circumstances have changed (after some time or some event).
I would use "I'll ask you once again" if I was going to ask the same question right away and after that make decision or do something depending on the answer I'll be given.
Does not the word ONCE in the phrase give it a subtext and limit the ways to use the phrase? Why would someone come up with once again if there is already again? I've analyzed the use of the once again and it is usually used when something was already done but the result is not quite as it was expected. The phrase is mostly used when the speaker is in the state of emot
I have already explained that 'once' is an intensifier, inbozz. As I said, there is not that much subtext. Occam's razor is satisfied. There is no call to inject changed circumstances and decisions. You are overanalyzing and thereby misleading the poster.