If it weren't for a recent retirement pre-funding mandate, the USPS would still be profitable. http://about.usps.com/who-we-are/financials/annual-reports/f...
Edit: Wait, that page says they'd still be at -$3B in 2010 without the pre-funding. And it looks like they haven't been paying into it since 2011. http://www.opm.gov/news/testimony/112th-congress/us-postal-s... So I guess I have no idea how profitable they are.