Why does my Kodak easy share C360 digital camera keep shutting off?

The battery is charged and memory card is not full (or at least it's not telling me that)

Also check the setting. Kodaks have an automatic shutoff that can be set to as low as a minute. And are you referring to the liveview disappearing or is the camera shutting off entirely.(I used to get think it was shutting off when it was just the liveview going off.) Liveview is also something you can change the setting to keep it on or turn off.

if you have a dock try putting it on there and turning it on, if it turns on while docked it might be that you need new batteries.

Premature turning off of the camera is due to low battery status. Merely recharge the batteries assuming they are rechargeables.

Good luck!

Did you drop the camera? I drop mine and it comes on
but then goes off. The cost to repair it was about as much as I paid for it.