Let me restore the interface
Many of you asked to implement State Restoration, a way to restore the UI state after the app is closed. After investigations, Paw actually works correctly, the problem many of you (including me) probably have is in the System Preferences. In the General section, uncheck: "Close windows when quitting an application", and it will do the trick.
Though, there is still a bug, that will be fixed in 2.0.6: the state of the Request List is not correctly saved when using groups (Collapsed or expanded state is not preserved).