Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
That is a puzzling problem, and must be quite bothersome for you. I hope I can guide you through to a solution.
I suggest first of all, that you remove the memory card from the Kodak camera. Check on the position of the 'LOCK' switch on it. What position is that switch in?
Try it in the not-Locked position (slide in the direction of the base of the arrow, rather than in the direction of the point of the arrow next to the LOCK switch.)
Then put it back in the camera, take a test photo or two, and see whether the test picture(s) is/are saved and still there when you turn the camera back On again.
Let me know how that effort goes, please, by Reply To Expert. If it doesn't work, there will be other things to try.
If it does work, I like to know when a suggestion of mine has turned out OK! so please inform me. Thanks.