I have cleaned and recleaned camera & lens contacts, installed two different sets of new batteries and checked the lense fit to the K-x, which is relatively snug and certainly just as tight as the K-5. While the 50-135 does auto focus on both the K-x & K-5, the 16-50 will auto focus on the K-5 but when the shutter release switch is depressed half-way or fully on the K-x the lens only cycles between infinity and 0.3m and not auto focus and not permit a photo to be taken.
I wish I could determine if the problem lies within the 16-50 lens or in the K-x?
Thanks everyone, for all suggestions. If anyone else should recognize this problem or have a suggestion, I am certainly willing to listen.

I had to replace the K-x batteries last week, Helios, no change. The battery indicator indicates that they are good, but I will install a new set just in case.
John Riley - I have been usinf Energizer Lithium batteries, as they normally get me through 2,000 or more shots.
You are right on JohnX, I did not clean the contacts INSIDE the camera mount, but will do so. Will also check the lens fit.
Hey Guys, thanks for all the helpful response. The wife is calling my name, so must run but will let you know the results ASAP.

The DA 50-135 is SDM and works well on the K-x.
I do not understand why the 16-50 will not?
I have re-cleaned the contacts and suffer with the same results.
Thanks JohnX your ideas are appreciated - have you any further suggestions?

Thank you for your response Archie. I do not understand how the 16-50 would work on the K-5 if it were faulty? I will clean all the contacts, as you say.

The lenses have an autofocus coupler (screw drive). For an example, I have tried the DA 50-135, DAL 55-300 and DA 12-24 and they work fine.
The DA 16-50 worked at first, and to my recollection has not suffered any abuse.
When I examine the contacts on the K-x I can see no difference compared to the K-5, so suspect not damage there. The same goes when comparing the 16-50 lens to other, the drive coupler and contacts all appear the same.

Hello there, I'm a newbie to this forum and I have a problem.
My K-x will not autofocus with the DA16-50 lens. Press the shutter release half-way down and nothing happens. However, all the other Pentax lenses focus fine on the K-x?
If I put the DA16-50 on a K-5 it works fine and there is no problem with autofocus. This problem definately has me scratching my head - hope someone out there can offer a resolution.