Just to close things off, I've logged onto the laptop, removed myself from wheel and things are working the way I want. However, if I run it from the menu and there are no updates, it simply tells me there's nothing to do and exits.
I never saw it behave this way (close itself). Maybe you should try clearing its config or maybe it's a side-effect of you first trying to open it when you were in the wheel group and now after you're not there any more (maybe reboot to 'fix' that?).