Screenshots often come out corrupted

I have a first generation Moto G (XT1033) with Android 5.0.

Often when taking screenshots, it gets stuck at the Screenshot is being saved message - then I have to forcefully close the System UI process if I want it to go away.

And the final file is corrupted (either the PNG file will not open on a PC or, for image viewers that are more tolerant to broken files, it will be black except for a small portion of the image). For an example:

See that the image is correct up to a point. It seems as if the file was closed before the system finished writing to it.

What can be causing this problem?