That would be the Industrial Revolution, as it often happens. It mainly has to do with the way it had to be obtained.

On the topic of salt-mining, the main reason for that is that mining salt is hard. Really hard. Prolonged exposure in the salt mines meant very fast dehydratation for the workers( either because of the constant salt dust in the air or just being around it). On top of that, excessive intake of sodium(salt is Sodium Chloride fyi) causes increased blood pressure which can lead to strokes or heart attacks. Because of these reasons, salt mining was a rather dangerous endeavour. As an anecdote, there is a russian saying from the 18th century back to the salt mines, credited to refer to punishing prisoners to work in the salt mines of Siberia. That probably means it wasn't too pleasant.

The other main way to obtain salt is from sea-water. This was used most commonly(or famously?) by the Imperial Chinese, who used this to at one point make up to 80% of all salt production in China. Of course, the method was, and is used, in many places around the world. In simple terms, this method means you take a lot of sea-water, put it in a pond, and wait for it to evaporate. The salt will not evaporate alongside the water, so you will be able to collect it. This was made increasingly harder by the lack of engine-powered machinery that made the transportation of sea-water a lot easier and safer, on top of also being dependent on the weather.

Another technique involving water refers to getting water with high-saline content, called brine, putting it in something, and boiling it. This was the most common method for obtaining salt for most humans for a long time, with evidence of salt-harvesting being found from 2000 BCE, in Zhongba, Chongqing, and going back to 6000 BCE, in Lake Yuncheng, Shanxi.

All of these methods are time consuming, manpower intensive and/or dangerous, all of which made salt a comparatively rare commodity, in certain places. With all these said, if I recall correctly, salt was not that rare, and I think it's rarity was overstated by the spreading of the "salary meant roman soldiers were paid in salt" as explained in this old thread I found in a 5 minute search. https://old.reddit.com/r/AskHistorians/comments/1f5wrj/did_roman_soldiers_actually_get_paid_in_salt/ . The thread quotes etymonline which says that "salary" comes ultimately from "salarium" in Latin which was the noun use of neuter of adjective salarius "pertaining to salt," from sal (genitive salis) .

At no point in history has salt been an expensive and rare ingredient. For thousands of years it has always been plentifully produced, both in brine refineries and in mining.

If you have heard popular reports of salt being extraordinarily valuable in antiquity, it was valuable in the same kind of way that soyabeans are valuable. A soyabean isn't valuable. The soyabean trade is colossally valuable.

To take a well-known example: the Romans. Roman brine refineries or salinae worked much the same as many modern ones, with shallow pools for drying out the brine in successive phases and then collecting the sediment into piles once they've dried out. No modern industrial technologies were required.

One important set of salinae was at Rome's own port, Ostia. Consequently the salt trade -- not a pound of salt, but the total production of the entire industry -- inland along the Via Salaria was important enough to name the road after the product. We know republican Rome had officials in charge of salt taxes. Again, not because it was a high price item, but because it was high volume.

Within the Roman sphere of influence salt mines also operated, notably in southern Germany and in Anatolia.

Now, a couple of caveats. It is true that throughout world history, in a handful of places salt has indeed been used for trade. By this I don't mean using as a replacement for coins, but using salt bars among a set of other commodities as a way of storing and exchanging value.

This never happened in Rome, contrary to popular belief. But it did happen with bars of salt in 17th-early 20th century Ethiopia, where salt could be mined plentifully in the Afar Depression; and I've seen less well-sustained reports of bars of salt storing value in other places too, like Angola and pre-Columbian Mexico, but it's pretty hard to track down reliable evidence and it's not my area. In any case, it was never a prestige object. No one ever made jewellery out of it or made it a prize for something. In Ethiopia, it was used alongside Maria Theresa thalers, clothing, and other commodities.

For the record, we can make a decent estimate of the cost of salt in republican Rome. It was cheap. Livy 29.37.3 reports that in 204 BCE, a Roman pound of salt cost a sextans, or a 96th of a denarius; and Polybius 6.39.12 reports that in the mid-100s BCE a foot-soldier's daily pay was ‘two obols’, that is, a third of a denarius. In other words, 330 g of salt cost about a thirtieth of a foot-soldier's daily wage.

If were to take modern minimum wages as a baseline, we could say that Roman salt was much more expensive than in present-day USA, but not ridiculously more expensive than some major modern economies:

Country	Minimum wage (8 hours or 1/365 year)	Salt price per kg	Source	330 g salt as fraction of daily wage
USA	58 USD	1.25 USD	Walmart	1/141
UK	65.68 GBP	2.71 GBP	Sainsbury's	1/73
Russia	399 RUB	23,9 RUB	Perekrestok	1/51
ancient Rome	2 obols = 1/3 denarius	3.03 sextantes = 1/32 denarius	Polybius, Livy	1/32

Edit: I wrote up a longer treatment on Roman salt in 2017 in this piece, and gave a talk in 2018 for which you can look at the slides here.

Edit 2: earlier I miscalculated the values in the last column of the table at the end. (Serves me right for not using a spreadsheet.)