Thanks for this video, the details are now clear. Based on the video, the half press works the same as when tapping manually on the screen (for focus, not the shutter).
It's not a focusing problem since the camera does not lose focus on the area you tapped on. Also, the movement is lateral, hence it is indeed the OIS. It does seem to release the hold on the lens after five seconds that's why the image drops a bit*, but then it slowly returns back to its initial position right after it drops. So the OIS does not stop after some time - it simply adjusts itself after five seconds. I'm not sure why that happens - it never happened to my L1020, not a single movement as long as my phone is still, both for the Nokia Camera and Nokia Camera BETA.
*- A "bit", but that amount of movement would definitely blur out your photos when the photo is taken right at the moment when the OIS adjusts. But given that the OIS "adjusts" five seconds after focus has been established and that the longest exposure time the Nokia Camera can do is four seconds, as long as you take the photo within a second after focus has been established you should have no problems.