I wouldn't have thought falling off at the rear was possible...
It is apparently possible, sadly...
is it falling off the smallest cog to between the cog and frame?
No, it falls off the derailleur jocket wheel/chain retainer. I couldn't find any clear pictures of the folded bike, so have used a non-folded pic from Flickr. Don't know if it makes sense?
Is the derailleur pulling properly to the back?
Not quite sure what you mean, but it seems to shift normally.