The other answer was absolutely wrong, so even though this is somewhat outside of what I am otaku-ish about I'll give it a shot, with sources this time.

We absolutely know that inflations have been a problem in the past. Starting with the ancient Romans to Mali to current day, inflation has been a problem. However, to truly answer your question you need to start with this first response: what does it mean for inflation to occur? (That is, what exactly is inflation?).

To summarize, inflation is when the general price level of goods/services in an economy rises, and what I think you're asking is not about inflation per se, but about hyper inflation, which is when an economy experiences very high and unusual acceleration of price inflation, whereby the purchasing power of one denomination of value drops rapidly with respect to all other items of value.

Previous theories argued that perhaps the Black Death caused some mitigated forms of rapid inflation as a result of labor shortages, although we think that monetary policy could also have been a factor in that as well. We absolutely know that hyperinflation was one of the main causes of the French Revolution, which could also be argued to be at the tail end of the transition from the Medieval Ages to the Modern period. These are only two examples of hyperinflation – Mali is another one, and we actually know of the Crisis of the Third Century, which was during the Late Antiquity period.

Sources:

http://en.wikipedia.org/wiki/Crisis_of_the_Third_Century

http://austrianeconomics.wikia.com/wiki/Inflations_in_History

http://www.economics.utoronto.ca/public/workingPapers/tecipa-463.pdf

http://en.wikipedia.org/wiki/Hyperinflation