I was under the impression that you can't use two adverbs to modify the same verb. Namely when again modifies "ask", once cannot also modify ask. I've been told that once can modify "ask you again", but I wasn't sure if that was correct/possible.
It seems alright speaking the sentence, but the more correct form would probably be, "Ask you one more time."
"I'm only going to ask you once more" is a more common way of saying this.
"I’m only going to ask you again once" is not 'wrong'. But it is unusual and as such may not be understood so quickly/easily.