"Control Panel" ("My Account" in BA 5.5) or "Login to control Panel" link on the final order placement screen (or the link at the top of the page when the user is logged in to the store) does not work for the existing customers. It results in:
The login/password combination you entered does not correspond to a registered user. Please try again.
However the same credentials work if you try to insert them manually.
The functionality is unavailable till BA 6.0.7 (implemented in the feature #PBA-68520).