I was having the same problem. After messing about with my phone for a while, I discovered that I didn't have enough open memory on my sd card. After I deleted three or four apps, and cleared out my cache and storage, it would then save. I have an HTC.
I bought the full version of MineCraft Pocket Edition for Android today and I've had to start over twice now because my worlds aren't saving. Does anyone else have this problem, or know why I am?
Had the same problem with HTC Desire C.
The root of problem isthat the MainCraft PE wants to save worlds in directory /mnt/sdcard/games/...(only?), but on HTC device - we have no any sdcards mounted to this directory ( /mnt/sdcard ). Internal storage is mouned to /mnt/nmmc (? or somthing like that ?)
For example, on "Samsung Galaxy Tab 2" we have internal card mounted there (/mnt/sdcard) by defauld (and the external SDcard is mounted to /mnt/extSdcard/ directory).
How to diagnisting that problem? install any file manager like TotalComander or other one , and try to enter the directory (/mnt/sdcard/ )
Ah, yes. I know what he means(I guess) because I have once experienced this. Relax everybody, I'm a doctor. Try downloading Root Explorer to see if the /mnt/sdcard is R/w or R/o. If it's R/o, well, it means read only, so you can't delete or add files in the sdcard and no, I'm not talking about the external sdcard. What I did is to turn on mobile data, uninstall root explorer and some file managers, and restart the phone. Wait, your in ios, but I mentioned Android, my bad. Well, You will never EVER catch a virus on an apple, so it is indeed true you are using the demo. (Holmes, you cracked the case!)