Maybe they aren't saving crazy amounts of money with fuel being cheaper. With the population growing, more roads, more housing developments, subdivisions, businesses, etc, they need more delivery vehicles, carriers, shipping centers and the such.
I've had excellent luck with USPS. Had a few hiccups but it happens when you think about the amount of mail they handle each day. Had good and bad with UPS and FedEx also.
Our annual population increase is only .7%. Gas prices are half what they were 2.5 years ago. If an organization isn't saving a large amount of money on fuel costs when fuel cost is a large part of their budget, that organization is messing up. I realize fuel cost for a large transportation company is far more complicated than just saying "fuel cost go down, so should price for service". There are some very complex calculations that go into most transportation fuel costs. That said, if we leave all that out and just look at the gasoline in the little mail trucks the savings USPS has come in to is quite clear. Average gas prices by year: 2013-$3.60, 2014-$3.34, 2015-$2.64, and as of today ~$2.00. In 2010 USPS reported using 650 million gallons of fuel. Let's say half that was for gasoline in the little white trucks. In 2015 that would have cost $858 million, in 2014 that would have cost $1.08 billion, in 2013 at peek average yearly fuel cost that would be $1.17 billion and today would cost ~$650 million. Even if we reduce the savings to half or a quarter of this example we are still talking about hundreds of millions of dollars in savings. And they still are raising prices.
USPS is still the best option for shipping. That doesn't mean it could not be better. It just happens to not be as bad as the others.