If your currency is too strong, you're probably paying your workers a lot more than workers elsewhere in the world. For a start off, this provides them with more disposable income than elsewhere, meaning they will eventually and inevitably bid against each other, raising the prices of goods and services. There is a higher cost of living in "rich countries" than in poor countries, the same product often for sale at a significantly higher price just because the local market can support that higher price.
Additionally, if your currency really starts to get very strong in comparison to some others, it seems to me it will be cheaper for your population to import than to buy locally produced goods and services (see: export of jobs to the Far East from The West over recent decades, unsustainable trade deficit problems).
An overly-strong currency not only undermines any export advantage you might like to enjoy, but also over time will gut your domestic economy.