Refrigerator drain tube clogged, I cleared it, it...

Question

14 year old Sub-Zero 550. The tube is in the back of the refrig compartment, starts just above the vegetable crispers and runs down the back of the freezer compartment down into the drainage pan.

I cleared the tube with alcohol, it clogges up again within 2-3 days. It is clearly ice, not debris. Tried several times and it ices up again.

I heard one possible solution: insert a copper wire down the tube and leave it in, so it transfers heat up the tube. But, not sure where to attach it to so that it would pick up the heat. Would this work? Is there another solution?

Thanks