its called carry trade. Traders will buy a currency with high relative interest rates, and sell the one with low relative rates in order to pocket the difference.
Logic says less interests will bring more demand for the currency, effectively RISING rates.
However this only happens when budgets are balanced and the economy is expanding/recovering.
What happens is that govt's print money, and there's more supply of this freshly printed currency when interest rates are low.
The main reason is that rates are usually lowered during economic slowdown periods.