Form is not rebuilding on "Add another item" in unlimited value entity reference field
What you are trying to achieve is Selecting Unique values from Multi Value Reference field... I do agree using default widget you may run into duplicates...

I would say consider using below one of the modules which supports entity reference using which you can avoid duplicate entries while adding..

You can choose one from variety of options mentioned in above article which suggests using of


Using of Multiple Selects.
Using of Chosen
An additional possibility is the Dynamic Multiselect Widget.
Another option is Entityreference Views Widget
There is jQuery UI Multiselect
Improved Multiple Select


Hope one of the above works for you :-)