Hey,
I tried this out on my account and created a new user, when I clicked Save & Close, the contact info was updated correctly.
Have you customized this screen? also, what browser are you using?
I used the Sales Order tab and the Activities tab link. I selected an existing activity, and then clicked on "..." beside customer. After entering in the customer info and clicking Save & Close, the contact information updated.
Please let me know the steps you took if they are different at all.