Why can one double bond exist in some resonance structures but two can't?
In your drawn example, the red-boxed structure requires the carbon atom to have five bonds, which, to channel my secondary school teacher, says "yuck, I don't like that".

This is a case of breaching the octet rule which has to with how the orbitals hybridise. Five full bonds on a carbon is not "allowed". However three full bonds and two partial bonds is common in both resonance and transition structures, and is in fact a much more accurate representation of the molecule you're drawing.

Don't forget too, that the location of the negative charge matters, and I can't see it in any of your drawings.