We have exactly the same problem that member nicknamed alex123 had four years ago using ad7656. His question is entitled "AD7656 occasional bad data" (it can be consulted through this link: https://ez.analog.com/message/74467#74467). In the answers to that questions, the same user (alex123) comments that they found the solution shorting analog and digital grounds. We have tried it but in our case, the problem hasn't been solved.
Do you know which is the origin of this problem and how to solve it?
Any help or suggestion would be highly appreciated.