You're right, but you're also assuming signals transmitted in isolation. The working assumption is that any technologically advanced society would be putting out fair amounts of radio constantly, the same way we are. This may not be the case, of course; they could have found a different technology, or simply used a different part of the EM band for communication.
But if they are putting out radio constantly, then we should be detecting them even outside a 50LY radius unless they just reached the radio age recently. The maximum distance would then be a combined function of distance, transmission power, and how long ago their radio age began.
True, my argument was just a simplificaiton of why the amount of time we have been listening would affect our chances of us having detected any signals, especially when combined with the fact that we don't continuously scan the same area again and again, which is why we might not end up catching one of the regular broadcasts.
The one thing that I've wondered about detecting alien signals is whether or not we'd actually be able to tell if it was alien or not. I know that scientists listen on a specific frequency that's related to the vibrational harmonic frequency of hydrogen (or something that sounds somewhat technobabble-ish) that is assumed to be what other aliens would choose, since it's easier to tell if it's artificial or not.
Assuming that aliens follow that logic, hopefully it won't be a problem to notice it. My problem with detecting radio signals is if we accidentally catch a signal that's not intended for us. How would we know if the signals that we pick are some kind of stellar phenomena or the alien equivalent of digital TV? BTW, that is a serious question, not a rhetorical one, since I'm under the impression that when the first pulsar was detected, it was confused for something artificial, due to it's regular signal.