the saving doesn't work

I recommend you read up about making bug reports:

2. Please provide a (to the point) summary of your problem. Avoid one worded summaries and things like "help!!!".
3. The description should contain details of the problem and how to reproduce it, so that we can more easily track down the problem and try to fix it.
4. Please search before creating a report to make sure your issue hasn't already been reported. If it has, please join the discussion there!

And looking at the title, you are failing at 2 and 3 only because 4 is not possible for reports after yours.

With your lack of detail, I'll help you, yet I could be more strict. These were found by searching.
1. Try to go to the main menu and select Settings -> Profile -> change File Storage Location to External. (This will make the game save your worlds and many other files to the Internal Storage, or sdcard if you don't have an Internal Storage)
2. As you seem to say there is no crash, it eliminates MCPE-20715, and possibly leaves generating 30MB+ of data in one session (MCPE-22478)