In fact,
without SR you'd really need to be shooting at a shutter speed of
1 / (focal length x crop factor)... so for 36mm, the shutter speed needs to be 1 / (36 x 1.5) = 54, which is roughly 1/60s.
With SR enabled, it depends on how steady your hold is, and the size of reproduction you're looking for, but 1/15s is possible, though pushing it. Personally, I don't have a particularly steady hold these days, so even with SR switched on, I tend to stick with a shutter speed of 1 / (focal length x crop factor) where possible, and when I drop to slower shutter speeds I take multiple shots and pick the best of the bunch.
Of course, in Auto mode, you don't have much control over things.
I suspect the reason your shutter speed is so slow is that you're shooting a slow-aperture lens at an ISO that is too low for the lighting conditions.
There's nothing wrong with the shutter on your K-S2. You're simply reaching the limits of your lens and the camera's Auto mode