I am having what I believe to be this exact same problem with my profile, except the city field is blank.
Adding a city name to the field and clicking Save does not save the city name- after a page refresh, the city name remains blank.
By mistake I entered my area name "Thaltej" before my city which is "Ahmedabad".
So I wrote like this: "Thaltej, Ahmedabad, Gujarat, India 380054" or something like that.
I went back and clicked on "edit" again but in the City field was still "Thaltej" instead of "Ahmedabad".