Hi my 2008 liberty am fm cd radio has just started cutting out, the audio part stays on for a while then stops and when i turn jeep off the audio comes back on any ideas.thks

Stock radio? no photo of it so how can I guess?
ok , so do tell what works and not first.
all 4 speakers cut out. left right front and rear?
all modes
am fm cd car drives ok, day and night all other features work on car.
yes, then the audio system head end (or amp if opted)
has problems.
this can be a loose or bad fuse to it,
or wires to it hacked, for sure if not stock, yah.
all radios can be bench tested.
a speaker. and antenna or CDDA cd disk, store bought.
sure can, done a vast numbers like that,

step one,
is it just a radio or radio with external amp?
step 2 is power to radio good, a voltmeter checks that easy.
if power is good to it then the unit is bad.
power means the power wire, and ground good. 12vdc key on. is good 0v is bad.
the other power wire is memory only.