Is it possible to fall out of love with someone?

We choose to love or. Not to love. The question seems to imply love is something that just happens but that's not the case. A great deal of information, experiences and emotional ups and downs go into "being in love". Loving is a commitment, a choice. When there is that much invested that commitment does not break easily. "falling out" of love is losing that commitment (choice) which breaks that bond.
Love. Absolutely. Happens all the time. However it depends on what you call love and how you define falling in love and falling out of love. Many people have quite varied definitions of these emotions.