Is it possible for a person to love some one and yet not to miss them when they are not around?

Absolutely. There are many kinds of love (8 according to the ancient Greeks) and not all of them are manifest as passionate heart longing when someone is gone. Additionally, everyone expresses love differently. It’s not uncommon to love family, but not necessarily miss them when they’re not around (or even sometimes be glad they’re gone). The same can be true of any relationship in your life.