How did "once in a while" come to mean "occasionally, from time to time"?
I understand it is an idiomatic usage, but "once" means "one time" and "while" means "in the meantime" , so how can the expression be used to refer to a number of different times?
Has "once" or "while" also other, possibly archaic, meanings? I could not find any in online dictionaries.
I think "once in a while" is parallel to expressions like "once a day," "once in every two months" that also refer to periodic events. The expression after "once" tells us how long it is between the different times; the action is done "once" for each of these time periods, but multiple times overall. I know people have made this point in other answers and comments, but maybe rephrasing it this way can help a bit.
"While" does not just mean "in the meantime." The first definition of while in the Oxford English Dictionary is
A portion of time, considered with respect to its duration; = time n. 1, 2, rarely 4 or 6. Now almost exclusively in certain connections (see below), the ordinary word being time.
We can see a similar use in expressions like "I'll be gone for a while" = "I'll be gone for a time period of indefinite but significant length."
It means one time (at least) in a set of times or a period of time (a while).
A while is an indefinite period of time. If the condition holds at even one moment during that period then the condition holds for once in a while.
Update (as suggested by @Cerberos) from comments I wrote here:
"Where is it said that once means 'at least one time'?"
"Once" means one time. I added "(at least)" gratuitously. Consider it removed, if you like. The phrase "Once in a while" means one time in an arbitrary (indefinite, nonspecific) time period. As such, it has come to mean repeatedly one such time in one such arbitrary period, that is, multiple arbitrary occurrences in multiple arbitrary time periods. Since the periods are arbitrary, it means, in effect, at least one time in an arbitrary period. If it occurs once in time period A and once in time period B then it occurs twice in the union of A and B, which is another arbitrary time period.
"yours is a comment rather than a real answer."
Fair enough. But you seem to think that "once in a while" is an idiom, and you wonder about how the idiom evolved. My answer is that a literal reading of once in an arbitrary while suffices. No real evolution ("come to mean") or "idiomatic usage" needed as a hypothesis. Same thing with "once upon a time", although we don't use "upon" here nowadays, so that is idiomatic now.
"I don't think the meaning is actually literal as Drew suggests. It should mean "one time in a period of time" not "from time to time"."
Actually, I did not suggest that the meaning can only be literal, i.e., that a literal meaning is necessary. I said that a literal meaning suffices - it can be read literally, and the meaning in that case is what one would expect. And a reading of "from time to time" follows from a literal meaning of "one time in a period of time" (because...because...time).
I tried to show how the meaning you understand is related logically to a literal meaning. That relation is as much of an "evolution" as I can come up with, I'm afraid. It doesn't pretend to be a real, historical evolution but is a logical becoming (relation between concepts). Then again, history can sometimes be underpinned by logic... ;-)
It's fairly straight forward.
In a literal interpretation it means that in a unspecific, but generally long period of time, this event will occur once.
It would be similar to saying:
Once in a hundred years the Oodjy Boodjy plant will bloom.
In practice there's an implication of variance on both the frequency and period of the event.
When we say 'once in a while' we're emphasising that
The length of the period is determined by the context.
For example if an astrophysicist said
Once in a while a comet will crash into a planet creating a large explosion.
he's probably talking about a period of hundreds of thousands, or millions of years.
Whereas if a biologist observing ants said
Once in a while one of them will run off course.
he's likely to be talking about a period of minutes.
"once in a while" doesn't really mean "occasionally, from time to time". That is the literal meaning, of course, but it misses the point of the usage.
"Once in a while" is an evasion. It is a way of deliberately not answering the question "how often"?
How often do you bet on the game?
Once in a while.
This usage does not deny that the person bets, but give no information about the frequency with which they do so. It is a way of answering without answering, a way of saying "I'm not going to tell you." without being rude.
Another example is "every now and then". Consider what the literal meaning of that phrase might be. What does "every now" mean or "every then"?
These are related to other non-answers, like "a little bit" or "from time to time".
The questions, therefore, is not how they came to mean something, but how they came to mean nothing.