It happens with gold, which could be viewed as a traditional currency.
Value is relative, so if you only value gold then the value of gold is constant. But if what you value is goods and services, then the price of gold is extremely unstable. You can see it graphed here (CPI being a metric of the price of goods and services):
Gold used to have a stable price in terms of dollars because the central bank pegged the currency to the price of gold, which I think is the reason people like Ron Paul believe that gold has a "constant" price. now the central bank pegs the currency to CPI so CPI is stable and gold floats freely (in dollar terms). This is preferable if you value CPI price stability more than gold price stability.
Also note that gold and silver often diverge in value relative to one another, so no matter what your perspective, it cannot be the case that gold and silver have stable value. If Somebody hits a rich silver vein then silver drops relative to gold.
What is the unit in which value is measured? There is no SI unit for value, and it seems unlikely that it would ever be possible to define one - it would basically require very surprising breakthroughs in psychology.
Hence people do the pragmatic thing and measure value in the currency that is predominantly used in their life. They use USD or EUR or whatever as their unit of value.
And in that sense, the value of gold and silver is clearly not constant, as a sibling comment explains.