Even if you took away the requirement to fund their retirement/pensions the Post Office would have lost nearly five billion dollars last year.
The pension funding is a common misdirection that is brought up far too often in discussions about the Post Office.
The USPS problems are
1) Congress, how many "corporations" have 535+ people to tell them how to run their operation. Congress routinely prevents the closing of obsolete Post Offices and Sorting facilities.
2) People simply do not use mail, dropping more than a third of the letters shipped in the last six years
3) Businesses are also dropping the amount of mailings made.
In 2006, the unfunded liability of the USPS was nearly 75 billion dollars. Who should be funding it? Certainly not the public. The law requires the USPS to put aside 5 to 6 billion a year. The issue that came up was, mail use plummeted.