There are a lot of reasons to believe that the value of our fiat money is losing its real value. We have inflation eating into the worth of goods and services that our money can buy and although this can be controlled to a certain degree this can never be stopped nor eliminated from any economic system. Another major problem is the tendency of many central banks to just print more paper money (termed as quantitative easing which is nice to ears) and circulate them to the economy. Coupled with a high degree of economic and political uncertainties as well as lack of trust for the government, we can in an era uncharted and which repercussions can be felt in the coming years.
Actually in recent months, inflation has been fairly low which is why the Fed is contemplating further rate cuts on top of what is already 2 rate cuts. Other world central banks are also pursuing easings of their monetary policy.
So it would be unfair to say that fiat is losing purchasing power right now, in the short term.
But in the long run, fiat doesn't have what BTC or gold has, which is a natural hard cap on the circulating supply, which is what should be concerning to asset holders. Not necessarily the short term depreciation, which doesn't always exist unless the currency is grossly mismanaged like in Venezuela or Zimbabwe, earlier on.