Translation:One more time.
I'm not sure google translate is such a reliable resource, though. Chinese>English might not be as bad as, say, Urdu>English (where the algorithm has a tendency to just give up and hand you an unrelated English word that starts with the same sound!) but I still wouldn't trust it with subtleties.
To me, if I told someone to "do it again" I would expect them to do it again once, not repeatedly. I would say "do it one more time" not to make sure they didn't keep doing it over and over, but to emphasise that it would only be once, for example if they had already done it several times already and I wanted to be clear that this would be the last time.
So my feeling is that although "again" doesn't explicitly contain the meaning of "once" it's often implied, and although "one more time" is a good literal translation of 再一次, it seems to me to be used a little more widely where "again" might be the more natural translation in English.
Any thoughts from Native speakers?
Breaking down the phrase it's literally: AGAIN (再) + ONE TIME (一次）...
I thought about it a bit more, and 次 alone simply designates the next in order, in other words, TIME!
再一次 = AGAIN+ONCE (one time) = ONCE AGAIN 再二次 = AGAN + TWICE (two times) = TWICE AGAIN
再见 = AGAIN + SEE/MEET ("to meet up with") = SEE [you] AGAIN ... or... [until we] MEET AGAIN
If we recall, there was a lesson about meeting/seeing one's doctor later, or a teacher seeing their student at a later time:
我下午要见我的医生。 I want to see my doctor this afternoon...
(I + AFTERNOON + WANT [to] SEE + MY + DOCTOR)
I love the patterns that emerge within languages!!
"Once" is definitely still alive and thriving in American English. "Once more" seems like essentially the same as "one more time", but it may not have been initially accepted because the literal translation seems to be "again one time" which more closely matches "one more time". I'm not a native Chinese speaker, but it seems to me "once more" should be accepted so long as there is not a different and better translation for that specific phrase.