Thanks for the report. You are using Reach, not Reach RS, right? I thought we have fixed this unfortunate behavior a couple of releases ago. Do you have the latest version?
The app is not leaving any files open, of course. And the project is saved every time you collect a new point. Something goes wrong when powering the small reach down. A shutdown button in the interface(which is coming soon) should fix this for good.
@DaneGer21, the workaround does not seem 100% stable to me. Just a warning.
Also, it would be great, if you could connect to your Reach and download the project files. You have a chance to restore your surveyed data and I will get some symptoms to work with. I described the process here.