How can I fix my GE Bottom freezer fridge?

Hello:

My 4 or 5 year old GE bottom freezer refridgerator has a problem. Every two or 3 days I need to turn it off and melt the ice forming in the small drain tray just below the fan which forces air up into the fridge. The ice isn't melting in the slot and builds up until the fan blades freezes solid in the ice.
The water is free to run down the slot. When I put the hairdryer to the ice it melts and just runs out freely into the back of the fridge so I know it is not plugged.
I don't understand what is supposed to keep this small drain tray free of ice.
What keeps the water from freezing when the defrost cycle goes on and flowing out of the fridge?
There is a small wire which is curled around the defrost element between the cooling coils and then runs along the tray to the drain hole but it isn't doing anything which I can see. The defrost "bar" is only a small coiled wire in a glass tube.

Can anyone help me with this? I've had two technicians out so far and they are stumped.

Herman