Why are my Citizens and peasants stuck in their status?

Make sure you have the required building materials to upgrade their houses. Going from Citizens to to Patricians requires 1 Tools, 1 Wood, and 4 Stone.

Source: http://anno1404.wikia.com/wiki/Patrician#Materials

Also note some of the other things said at the link above for possible reasons why advancement has stopped:

Common reasons the population does not advance is that the population does not have all items needed, the population is being taxed too high, or there is not the correct proportion of each class. Unlike Anno 1701, you can't get far at all if your civilization is only peasants. Citizens need peasants to live, patricians need citizens and peasants to live, and so on. To determine how many houses can still ascend, click on the city's market place and look at the pyramid. For example, if it shows there are 31/31 noble houses, it means you've reached the maximum number of noble houses.