I have been cooking yogurt cakes in the US for a while and each time it has to cook for an extra 20 min. Why?

My first suspicion would be your oven. Home ovens are notoriously inaccurate, and it may be that yours is just slow, which is to say that it doesn't quite reach the temperature to which you set it. If you don't already have one, buy a good oven thermometer (the kind you leave in the oven all the time) and use that rather than the indicator on the oven knob or the oven's display. You may find that when you set your oven to 350°F, you actually only get 310°F.

The second suspect would of course be the ingredients, especially the flour. Flour varies a lot between countries, and the fact that you're using American flour and also changing the quantity could impact cooking time. You also didn't mention what type of flour you're using -- common types in the US include all purpose flour, bread flour, and cake flour, and these each differ in protein content. One thing you could try (after checking your oven temp, of course) is to use French-style flour and see if that makes a difference. If that does the trick, then you might experiment with blending two flour types (like all purpose and bread flour) to approximate the protein level of the flour that you're used to. Yogurt also seems to be different in different countries, and it could be that ours has a higher water content than what you're used to.

All that said, if you like the cakes you're making, then perhaps there's no need to adjust anything. A good cake is worth an extra 20 minutes of waiting.

Note: as Sobachina points out in a comment, altitude can make a difference. King Arthur Flour has a summary of changes to expect if this could be a factor.