No, you should not. Adaboost can indeed pick the same feature more than once per boosting run, but usually the feature will have a different weight value (alpha value).
The results you're getting might have many different causes. For instance, you may have a bug in your Adaboost code. You may also have a bug in your features or weak classifiers. Or you're not providing enough samples to your boosting algorithm. Or, your weak classifiers are too weak. Or your strong classifier is overfitting really fast.