Do you mean it's a sibling or parent? My family is super small, so to me, my mom's sister was pretty close. I have one brother, many years younger than me, who lives across the country from me, near my dad. The fact that I live about 12 miles from my aunt and have never run into her (I ride by her street a few times a year) amazes me. But, her world is very small.
Sometimes it's hard not to be with family on holidays, for me, especially Jewish holidays. But, we have been sharing holidays with friends for many years, and they have become our family. Of course, my kids, I think would like to continue contact with my cousins, but haven't, knowing how it would upset me.