Power washing is the best way to remove the loose coat of paint. Not all will come off but I suspect most will. After preping the cinder block all you need to do is prime with a good oil based primer and repaint with a good acrylic paint. Priming was the missed step that led to the failure you are experiencing.
* Using a power washer isn't easy. Be careful if you decide to do it yourself.
* If you don't already own a power washer you can rent one. Only buy if you think you will need it for other chores.
* Check with your local paint store for a good exterior primer. You could also use a good acrylic primer, like Zinsser 123, but an oil base will stick for sure.
* Go to a real paint store for your primer and paint, not a hardware store.