It may be a power issue, but I'm fairly convinced it's not a bad batch of batteries.
The reason I say so is simply this:
I've had quite a few of these batteries (all genuine Pentax). Battery #1 and #2 are as old as the original K5 (3 years old). Battery #3 came with the K-01 (bought 1 year ago). Battery #4 came with the first K3 bought in November. Battery #5 is from the K5-II that Pentax loaned me (don't know age). Battery #6, in late December, came from Pentax directly, to attempt to reproduce the problem with the newest battery possible. Battery #7 is an extra I had purchased sometime last year (early 2013). Battery #7 came with the second K3, that I got in February of this year.
So I've had a whole variety of genuine Pentax batteries with varying ages, and all of them produced the mirror flapping.
And then there's at least one report of the issue happening with the Power Adaptor. It seems to happen with or without grip, with AA batteries, 3rd party or genuine Pentax batteries.
So I'm fairly confident, that the power supply itself doesn't seem to be the problem. If it's a power issue, it's on the camera side, and the way it's handling the power load. The EXIF data from photos doesn't seem to be capturing any spike or drop in power that I can tell, all seems normal there, so if there's a spike or drop that the
camera can't handle, it's not coming through the EXIF data.
I don't at all think it's wrong to investigate power issue... all avenues should be explored. However, a bad batch of batteries would have to extend to basically all batteries manufactured since the original K5 to coincide with my own experience, and wouldn't explain the issue showing up with the power adaptor.
I would seriously like to know what is the difference between the K5-II/s bodies and the K3 as to show this fault in the K3 but not the K5-II/s bodies. To me, it seems, this is an important area of investigation. It may still come down to a power issue, but there would obviously be something different in how the two cameras are handling that power load, if it's indeed power related.
An interesting post on the issue with the original K-5 related to the aperture mechanism and power.
Worth a read if you want.
Oh, and JHMos, was it that the camera wouldn't power on, or just wouldn't hold settings? I seem to remember that it had something to do with retaining settings after being powered off, not that it wouldn't run at all... but I might be remembering wrong.