PD 6 on Lion requires Admin password on each Launch

I'm running Parallels Desktop 6.0.12094 on Mac OS X Lion 10.7.1. I am always logged into the Mac OS without administrative privileges.
Since I've recovered my computer from a Time Machine Backup, Parallels Desktop asks for an admin username and password twice(!) each time I launch it (see screenshot below):



This wasn't the case before. Have you seen similar behavior, and do you know how to fix it?

 

I got this same roblem on PD 11 / OS X 10.11 ("El Capitan").

Any solution?

I want hte VM to be launched on system startup, so this stops it, waiting for an admin password.