Saved client details in an invoice (Name, Address or E-mail address) stay saved even when you change your Client data. Changing client details shouldn't change your invoices retrospectively, that would create quite a mess in your documents.
If you need to change client's details on an invoice, proceed as follows:
In the Client's list edit the client and change its details - name, address, e-mail
Edit the invoice and select another client (any client will do)
Save the invoice
Edit the invoice again
Select the right client
Now the actual data from the client has been refreshed in the invoice, and you will see the desired client's details.