The answer is, unfortunately, not very long. The SAMi app is continuously streaming video and analyzing for motion so it uses a lot more power than your typical app.
We've seen a run time of about 2 1/2 hrs on a fully charged 6th Gen iPod touch while the SAMi app is locked. Your results will vary based on many other factors including the particular iOS device you are using, the WiFi signal level, and the screen brightness. SAMi can be configured to alert you when the battery is running low.