Most probably Replay Media Catcher checks whether the program is registered or not, and checks for updates. I don't think the registration should be checked once only, because otherwise it would be easier to make a cracked version. And I don't think Applian needs your IP address... what would they do with it anyway?

p.s.
You can ask this question in the official Replay Media Catcher forum or you can submit a support ticket at www.applian.com.