Problem: While adding test cases to the existing Test Run original test case assignments are being reset.

Solution: The actual issue here is if the full test run was assigned to a user, when it is edited again in the future the assign to field will default to that user being selected in the dropdown, and when saved will re-assign all tests within to that user. The trick to prevent that from occurring would be to make sure that the "assign to" field is not set to that user's name, but instead to the blank entry at the top of the selection. This will keep all assignments set to their current users when the edits are completed and saved.