Difference Between ‘Once a Year’ and ‘Once in a Year’ – Prepositions and Time

There is a slight, but meaningful, difference.

"Once a [time period]" implies frequency observed over a range of time greater than [time period]. "Once in a [time period]" implies an observed frequency of 1 in a single [time period].

If somebody were to say something occurred once in a month then he means he is talking about an event with a time of a month. If someone says something occurs once a month then he definitely has data larger than a month.

Example:

My last boyfriend, Eric, would buy me flowers once a month! But John has only bought me flowers once in a year. Does John hate me or is he just less sentimental and thus will only buy flowers for year anniversaries?

Another example:

During the first year of our relationship, Phillip bought me flowers once a month. Why would he now only buy me flowers once in a year?

As FumbleFingers brings up in the comments, the "once in a [time period]" could instead be an application of figurative speech and not based on technical data. The following example shows a usage of the phrase that indicates exaggerated speech is at play.

Wow! That's rare; it only happens once in a blue moon!

This is perhaps more indicative of a common idiom but still important to bring up.

To slightly elaborate on what was established above, it may not be obvious that the phrase "once in a [time period]" can be used to establish a cap on repetitions in a [time period]. See below.

Alice: "So, he goes to Mexico 10 times a year?"

Bob: "Yes, but never twice in the same month; he only goes once in a month."