[Solved] How to Fix Problem with storage device error in Grand Theft Auto V

I had exactly the same problem and none of the suggestions online worked. One thing I can say for certain is that it is NOT a defective disc.

Here is how I resolved the problem:

1. Delete the existing copy of GTA 5 from your Xbox. (I deleted any saved games as well as a precaution)

2. Clear the system Cache (as recommended by Rockstar)

Press the Guide button on your controller, go to Settings, and select System Settings.
Select Storage or Memory.

Highlight any storage device, and then press Y on your controller. (It doesn't matter which storage device you select; the cache will be cleared for all storage devices.)
Select Clear System Cache.

When prompted to confirm storage device maintenance, select Yes.

3. Ensure you have enough memory on your hard drive.

4. Ensure that cloud storage is enabled

From the Xbox Dashboard, go to Settings, and then select System.
Select Storage, and then select Cloud Saved Games.
Select Enable Cloud Saved Games.

5. Insert Disc One and install Game

This is where I think the problem lies. Once the game has installed and you are prompted to insert disc 2, do NOT insert disc 2.

Press the guide button on your controller and go back to the xbox home page. (I actually switched my Xbox off and then back on again.)

6. Insert disc 2 and start playing the opening mission of GTA 5

7. As soon as you are able to save - I think this is once you have safely recovered the two sports cars in the Franklin and Lamar mission - you will be given an option to save to the hard drive or the cloud. SAVE TO THE CLOUD.

I have been playing GTA 5 for 2 days now and the game has not restarted once. I hope this works for everyone.