I've been restoring messages to a new phone and I realized, after leaving the phone running for hours, that when the screen times out, the import process stops and then starts again when I wake and unlock the device. So really, it's just been running for five minutes and then stopping when the screen times out and then running again when I wake it, make the process incredibly slow. I have a lot of messages and the whole process is about a couple hours anyway, if there were no display timeouts interrupting it, but would have been done long ago if I had realized the problem.

I have now set the screen time out to 30 minutes, while the import is running, and I'm keeping an eye on it. But shouldn't the app keep running regardless of the display timing out? I have battery usage set to unrestricted, so I don't know what else I can do except keep and eye on the import process and make sure I interact with the phone every 30 minutes so it stays awake.