The short answer to this is that it's updated all the time and it's dependent on the popularity of each keyword.
The more popular a keyword is, the higher the search volume, the more frequent will be the update for the relevant data relating to a keyword search.
The data we are referring to here includes traffic value, search volume, keyword difficulty (KD), CPC, organic traffic and position on SERPs.
Please read on for the full explanation.
We calculate the Ahrefs' traffic value by multiplying the monthly organic traffic of each keyword at the respective ranking position by the CPC value and then adding up the organic traffic cost of individual keywords that the target website/URL ranks for. (Find out what does the traffic value metric mean.)
And we calculate the organic traffic of each keyword at the respective ranking position of the target website/URL by multiplying the estimated search volume of the keyword and the unique CTR of the target website/URL's position in a SERP.
You may also be interested to know that we estimate the unique CTR based on the CTR distribution curve. (Find out how we estimate the CTR.)
So with all these in mind, we update the search volume, CPC value and recompute CTR distribution curve once in a month.
But since CTR depends on the target URL/domain's position in a SERP, which we update once in a few days to once in 1-2 months (depending on the search volume for the respective keyword), there is no concrete point in time when the traffic value for the target URL/domain is updated.
In other words, search volume, CPC value and recomputed CTR distribution curve of a keyword are updated once a month.
Metrics like KD, organic traffic and hence traffic value are dependent on the position on SERPs and hence updated once in a few days to once in 1-2 months (depending on the search volume for the respective keyword).