The Rogers surname is so common,I have lots of my ancestors whose deaths I have never found.You can only narrow it down by using all the censuses and see if dad is named as deceased on marriage certs,or if anyone remembers if they came to family occasions etc.
Up to 1911 middle names were entered in the indexes in full,after that until 1969 they only used a middle initial,making it even harder with a common surname.
And as Ann only has the one name,as do a lot of my Sarah Rogers's

I think you will have trouble pinning her down for sure.
Carol