Thank you for your suggestions. I got the point. After a couple of days experimenting and testing, I can say that the sample code provided is working. It just does not address the weekday setting, meaning the weekday is not set and therefore it seems to repeat the initial day it set itself when powered up the first time. The time and date, which is addressed in the sketch is changing properly.
Setting the RTC manually with Wire.send() seems to solve the problem. At least for 1 day change over testing.
Thanks again