There are generally two reasons why a planetary atmosphere can lose density (which isn't quite the same as pressure, but I suspect what you really want to know about) - temperature and leakage.
Let's deal with leakage first.
Both Mars and Venus, surprisingly enough, are losing atmosphere at a steady rate. This is despite Venus having an atmospheric density of more than 90x that of Earth, and Mars having less than 1% the atmospheric density of Earth. Why? Neither planet has a magnetosphere.
Ultimately, the solar wind is actually a thing. Highly energetic charged particles leave the sun at a reasonably constant (or at least rhythmic) rate, and they can do a lot of damage to whatever they strike. The Apollo astronauts experienced flashes in their eyes while in space and didn't tell their medical staff about it until after they landed in case the mission got scrubbed. These flashes actually turned out to be cosmic (read solar) rays striking the retina, triggering the flash, and doing some damage on the way through the body. This is similar to how Xrays work in point of fact.
Those energetic rays, if they strike atmosphere in a significant quantity, cause it to deflect into space, meaning that without a magnetosphere to protect it, most planets reasonably close to the sun (terrestrial planets) will lose their atmosphere over time. Mars has been doing that for some time, hence the very low density of its atmosphere.
This is where the similarity between Mars and Venus ends however, which brings us to the next factor; temperature.
Bottom line is that the same volume of gas in the same sized container is at higher pressure when hotter than the other container. What that means is that in the case of Venus, the density is high because the temperature is high; the amount of CO2 in the atmosphere in Venus' early life was enough to start a runaway greenhouse effect, and the increase in atmospheric temperature resulted in an increase in atmospheric density. Highly energised gases have higher density, but the converse is also true; gases at lower temperatures experience lower densities.
So, the answer to your atmospheric density question is one of the following, or a combination thereof;
1) Temporary Reduction of Magnetosphere Strength
If the magnetosphere of your planet, for whatever reason, reduces in intensity, the cosmic rays that are let through could lessen the volume of gas in your atmosphere. Could that happen quickly? Probably not, but a combination of lack of magnetosphere and (say) a Coronal Mass Ejection (CME) event could trigger some wholesale losses of atmosphere. It would be very unlucky for some temporary event in the Earth's core to stop the inner core spinning enough to generate the Earth's magnetic field at exactly the same time that the sun enters a highly unstable phase of mass CME's but the odds are not mathematically zero.
2) Lower Overall Temperatures
Believe it or not, your Snowball Earth may actually provide the answer to your question. If the Earth has a high CO2 content and a high overall temperature as a result, then plants take that CO2 and convert it back to oxygen, it's possible that the atmospheric pressure could reduce significantly as the temperature falls. Could it fall by 50%? Highly unlikely but not impossible. Given the temperatures on Venus and the massive density difference between Earth and it, it's certainly within the realm of possibility that atmospheric pressures as a result of a Snowball Earth could halve, although a lot of that would depend on how much CO2 was in the atmosphere beforehand and what impact that had been having on global temperatures in the first place.
Of the two of these phenomena, the first is the most likely to generate a dramatic change, say over your 20 year span. The second is more likely to have a stable but reversible effect over a long period of time; it's postulated that our own Snowball Earth was relieved by volcanic activity for example. The magnetosphere on the other hand is highly unlikely to stop and then restart at some point, especially when you realise that the magnetosphere is ultimately the effect of the inner core of the Earth acting as a very large dynamo; better for it to just keep running.
That said, if the sun was to go through a REALLY unstable phase, super CMEs might release enough ejecta to overwhelm the magnetosphere and strip away a lot of the atmosphere. If you want a sudden (read as over the course of a few days) drop in atmospheric density, one that you don't mind if it can't be reversed, this would be a definite candidate. Of course, the catch is that a star that has those kinds of awkward moments is unlikely to be trusted by the universe not to act up in a way that would prevent the long term evolution of intelligent life over time, meaning that this scenario too has the discomforting ring of improbability to it.
Remember of course that the Earth is nearly 4.5 billion years old and we don't believe this has ever happened to it despite the sun being decidedly middle aged. That said, if it was to happen, these are the scenarios I can think of that might actually cause it.