Mysterious Disintegrating Udon noodles
Organic merely tells you that the wheat that was grown, was grown in a more environmentally friendly way, ie. without the aid of pesticides.  That on its own will have no effect on noodle stability.

They may be poor quality noodles, have gluten level issues, are they also wholewheat, do your regular udon have some form of strengthening additive like with ramen?  Many noodles have kansui added, or whatever passes for that chemically (sodium carbonate) added to strengthen the dough.  Of course it may not have been kneaded enough, too old, too dry.