Do I need a new SSN to upgrade to a later version of UniBasic?

A new SSN is not needed to upgrade to a later release of the same major revision. Thus, a new SSN is unnecessary when upgrading from UniBasic revision 7.1 to revision 7.2.
A new SSN is, however, necessary while upgrading to a new major revision. Thus, a new SSN is needed while upgrading from UniBasic revision 6 to revision 7.