The Fixed Exchange Rate system collapsed in the 1960s because of
1. High oil prices.
2. This led to high inflation in the US and a consequent deterioration in the value of the US dollar. The US could no longer fix the exchange rate of the dollar to gold as the exchange rate value was way out of line with the domestic value of the dollar (which had been eroded by inflation). As a result, the US abandoned the fixed exchange rate system.
3. Once the US abandoned the system, it was no longer sustainable and other countries also abandoned it.