Custom field set data not being saved if contact has more than one contact sub type

If you're using multiple contact types for contacts, alongside custom
field sets available only to each of those types, one of them won't
save in edit mode.

For example:

A contact has contact type 'staff' and 'parent'

Civi is setup so 'staff' have a custom field set with some questions, and
'parent' have a custom field set with some other questions.

In edit mode for the contact it will only record the changes to one of
those custom sets of questions.

You can still edit and save the field set successfully in view mode.

Found on a 4.4.13 site and replicated on the demo 4.5.8 site.