Am I tone-deaf?

Ok, so the title is only half-serious. Anyway, I find that when listening to native speakers (and fluent non-native speakers) speaking at a normal pace, I cannot detect the tones at all (well, maybe a little). So, when interpreting normal dialogue I have to go off of the pronunciation (which I have no trouble distinguishing) and context alone. Is this normal? Does anyone else share my frustration?