In my best mythbuster voice.. "well there's yer problem"
The frost is insulating the cold face.
The air in the box may be 12deg but the cold face is below zero, hence frost.
A small computer fan, 40mm or something like that, will keep the cold face warm enough(by cooling the air blowing over it) to stop it frosting...
Even better would be to mount a small heatsink on the cold side with the fan mounted to that... a smaller version of whats on the hot side.
Have fun
