Yeah, I put mine down all the time. I keep hoping someone will take it. But, they don't!
So do I.I do not let my handbags out of my sight, unless I have someone watching it.
This thread reminds me of that episode of Sex and the City when Carrie's Manolo Blahniks were stolen from a party in her friend's house. I wouldn't leave any of my possessions unattended at a party anywhere! I'd only feel comfortable with that if it were a small gathering of people I knew very well and trusted. Other than that, I generally trust no one.
I do not let my handbags out of my sight, unless I have someone watching it.