It may not be a problem with your bank account but with the VISA card.

There are 3 big Visa types:
~ Visa Classic (or International)
~ Visa Europe (or VPAY)
~ Visa Electron

If you hold a Visa Europe or Electron, the transaction will likely not work.
VPAY and Electron have a different verification process for transactions who is not very "compatible"... well that's why they are cheaper, probably a business thing.