FooBar is quite right that unless you expect GDP growth to stop, fixed nominal supply currencies will lead to deflation.

A moderate degree of currency inflation serves a number of useful functions in the economy. The two most obvious are:
 - It induces people to spend their money before it loses its value. In a deflationary environment there is an incentive to put money under your mattress and spend it in a year when it has greater purchasing power. If everbody does this then the lack of demand will lead to a decrease in overall economic activity (i.e. a recession).
 - It provides a weapon against downward nominal rigidities. For example, workers are generally reluctant to accept a nominal pay cut, even if market conditions are such that the current wage is above the equilibrium level. Inflation means that their employer can simply increase wages at less than the inflation rate so that the real wage is decreasing.

Without inflation you miss out on these benefits. The first benefit might not seem like a big deal if you think you can simply set the rate of inflation at zero percent. But it is very hard to hold inflation constant at some target level so attempting to hit zero inflation will almost certainly result in occasional lapses into deflation, with the attendant negative economic consequences.