Hallo Hans,

I know it sounds strange, but certain ADC react indeed with systematic failure on stray coupling. It's of course unprobable to get such a stable failure performance as you observerd. But such systematic failure is possible and was observerd many times in the past. The reason is, that with heavy stray capacitance you get some feedback from ADC, giving you exactly at the wrong moment the extra portion of charge injection. Stray coupling is different from noise: Stray coupling has some correlation, noise is uncorrelated. From uncorrelated noise, you wouldn't see such systematic failure, of course.
I did experiment some years ago with 80C552 and noticed that it's ADC is very sensible to such feedback. The only cure is to have some low pass filter connected as close as possible to mcu. Remember datasheet of 80C552 which states, that between machine cycle 8 and 9 input signal is not allowed to change, at all. But if stray coupling injects charge right at this moment, you will get very strange conversion results, showing some specific ystematic failure.

Datasheet of PCF8591 does not tell anything about input characteristics of ADC. No input resistance is specified, only some leakage current. That's strange and demonstrates, that input resistance is extremely high. But this also tells something about suscebtibility of input against stray coupling: Extremely high. Unfortunately datasheet does not recommend any sort of measure for dealing with this extremely high resistivity. No information about anything (typically for philips). Have instead a look at datasheet of some MAXIM ADC. It's a real eye opener. Even information about necessary settling time of driving operational amplifier is given.

I hope that you will never see this failure again. But if so, please remember me and the recommendation about input filtering.

Regards,
Kai