Your LDAP sync is creating a Joomla user and not a CB user. So the user exists in Joomla, but does not exist in CB. You can temporarily fix this by running the Synchronize Users tool in CB > Tools, but your LDAP sync implementation should be adjusted to create CB users. The API to do this can be found below.
www.joomlapolis.com/documentation/127-community-builder/279-tutorials/18362-registering-a-user-through-cb-api
CB however doesn't handle password storage. Joomla does. Does this happen only for LDAP synched users? Do normally registered users have this issue?
Enable debug mode and maximum error reporting in Joomla global configuration then retry saving profile. Next provide the full call stack for that error so we can try and identify where it's coming from more specifically.