Rear hatch window latch

Do you mean the glass comes down and latches or that the latch itself closes? If it is the first then the gas struts are bad. If the second then the latch spring is binding or broken. As a test, get a small can of spray lube and spray the latch and spring assembly and open/close the glass a few times to work in the lubricant. If the spring does not free up the latch assembly would need to be replaced. There are a lot of Liberty's out there and the rear glass latch is the same from 2003 to 2007.