I'm also having this problem, and none of the QB employees seem to be understanding what we're talking about and keep offering solutions that don't work.

If we try to add an invoice to a project by changing the Customer field to Customer:Project, it will completely reset the invoice and all line items will be removed.  This happens regardless if there are payments attached.

All we want to do is change Customer  to  Customer:Project without resetting the invoice.  It works with estimates, not with invoices.  Hopefully this is clear.