The important point is that the "price of money" is depending on this demand for store of value (in that particular monetary asset).  That demand will vary according to the mood of people, and also according to the kind of monetary asset that is mostly "in" (that is, what people speculate that others will still want to accept, and at what price, later when they will want to get the value back).
As such, the value stored in a monetary asset is normally fluctuating.  One day there may be a high demand for money, and money will be worth a lot ; the next day, there may be a much lower demand for that kind of money, and it may become almost worthless.
In a fiat system, this is mainly stabilized, essentially by imposing monetary monopoly (merchants are obliged to accept that type of money against their goods and services), and by introducing feedback mechanisms with the central bank, buffering the money offer against the money demand.