My Brazilian wife is leaving me and going back to Brazil, She has a Green Card, but has no intention of coming back to the US. We were married in Brazil in 2003, but she has only been to the US a few time for weeks at a time (4 weeks in the last year). Since she is deserting me, am I responsible for her financially?

Get a lawyer and file for divorce on the grounds of desertion. Should end any obligations right there.