Connect ID system does not store person registration's history. At any given time, only one registration per discipline can be stored in the system* and no time information is available for it (e.g. date_from and date_to). It implies that when a new registration is added for the same discipline it replaces the previous one. This happens regardless of whether the previous registration has been active or inactive. Previous registration is removed from the system and cannot be retrieved.
This said, some information about past operations on a person are actually stored in Connect ID Log called Audit Trail. It is accessible via Admin Console - note however, that a view is filtered based on access rights, which means that a new_MA will not see the operations done by an old_MA.
The fact of not storing data in a centralized database should not, however, be seen as a limitation. Registrations history should be kept by Member Associations in their systems - and from those systems history can be retrieved. It is done automatically by an SDK when a duplicate is found for a person being registered. Request for details of duplicated person is sent to other MA and personal details (including registration history) are sent back in a reply via Service Bus - without the central database knowing about personal data of a given person. More information about this process can be found here: How to integrate with FIFA Connect ID (especially in the presentation attached).
* Exception from this rule is Beach Soccer - using this discipline, person can be registered in several MAs at the same time.