Pentax

I have an older DA50-200 which has loads of issues focussing around the infinity point. My K20D tries to focus beyond infinity especially when the contrast levels are not all that high. When I was on vacation I had to use it in manual focus most of the time.
Is this something which can be corrected in the focus adjustment setting for this lens?

Some lenses, especially telephoto ones, do focus beyond infinity. This helps to compensate for a shifting infinity focus point with changes in ambient temperature.

Later camera bodies than the K20D allow focus adjustments on up to 20 lenses to be stored in the camera memory.

I don't mind if it was able to focus beyond infinity but with the 50-200 it can't move beyond that point even though the body tries to and so it fails to get a focus lock and refuses to take a picture unless I set it to manual focus.