You’ll need to get that paint off. Likely, there was no sealer put on the blocks and no primer.
So, get the paint off. Then use a sealer (your local home hardware and paint store can help you with your choice).
Once you’ve put that on, let it dry according to the directions.
Then, using an oil-based primer (Bull’s Eye 1-2-3 or Kilz), paint the primer. Use 2 coats and not just one.
Paint any kind of paint on top of the primer. You can use latex paint too.
When the paint was orginally applied ,there was probaly no sealer applied,since your basement is below frost level,id strip the paint ,apply a water barrier type sealent,then paint over. You should be okay. Im thinking whatever little mositure is coming in contact with the cinder blocks is causing the paint to bubble. You can use a oil based paint on top of the water barrier to provide some added protection. Good Luck.