One problem related to engine burning oil has been reported for the 2010 Jeep Wrangler. The most recently reported issues are listed below.
Heavy oil consumption 3-4 quarts every 2000 miles . . I bought the Jeep new in Aug. 2010 it has 48200 miles on it. . It is just out of warranty. Took it to the dealer and called Chrysler. They wont do anything and told me they have never heard of that. So I took it to a local machine shop and they told me that the piston rings are sticking to the pistons allowing oil into the combustion chamber. Their are many complaints online about this exact problem.