In situations like this you have to use a tripod and preferably 2 second time which will automatically cancel the shake reduction, which is what you want when working on a tripod.

If you are more likely to pick it up and take it with you then I'd think it's a keeper

That looks like camera shake to me.
I have the K-S2 it's a great little camera but even in auto there are parameters that can be changed/set. I would guess you do not have auto iso selected so the camera has opened the aperture as wide as it can and the only place left for it to go to get the correct exposure is to slow the shutter speed right down, allowing for camera shake. Press the iso button and ensure auto iso is selected this will give the camera the ability to adjust to a higher iso and keep a faster shutter speed thus reducing the risk of camera shake.
If this is not the problem let us know and we'll get it sorted.
Also the camera shake reduction system can be turned off in Auto, press the info button and check that camera shake is on.
Best
Nigel

Very nicely handled set

So pleased others are enjoying my little idea, it gives something different and with in camera blending of multi-exposures is a doddle to do. Perhaps I'll be seeing some examples from others sometime

Thank you for having a look, commenting and liking. I have to say I didn't really know what to expect but, am very happy with the end results.
1st taken with the very capable HD DA 55-300 WR, Second two the excellent DA* 11- 18mm

Lovely

The Kx was my first DSLR, I owned it for about a day, founded exactly this problem with rechargeable AA batteries. I took it back to the shop and got my money back, a very disappointed chap. I believe non rechargeable AA batteries work better but a bad mistake to make by Pentax in a camera that only takes AA batteries.
I can offer only sympathy.

Shame the size of the images is so restricted but you get the idea.

From my recent trip to Bempton Cliffs, Yorkshire, UK
In camera Bright blend mode, raw, first one is 8 exposures the second two 18. With the small buffer on the K-S2 there is a pause after 10 raws then it resumes more slowly which can be seen in the images but, they give a different take on the movement of the birds which in these images are mainly Gannets.