Depending on your problem and your choice of selection operator, I think this could be normal behavior. Your population size is large enough that for an easy problem you are converging very rapidly on a solution, and your selection operator is letting those good solutions take over the population.
I am not very experienced with evolutionary computation and I am wondering if I should worry about the behaviour of my setup. From one generation to the next generation I get more and more identical individuums. This happens very rapidly. My Popilation size is 3000. For example some individdums of generation 1 appears ten times in generation 2. At generation 10 I have some individuums wich appear over 50 times. At generation 20 the whole population consists basically of only one indiviuum. The diversity of generation 0 looks ok. So I have enough structure to get enough different individuums, but something happens during the breeding. I am using pretty much a standard setup (all the "simple" stuff). I am little bit overwhelmed by all the parameters, so maybe someone can give me an idea, if and with which parameters I should play to change the described behaviour.