It's often recommended to flush the drain tube out with water and bleach solution with a turkey baster to put some pressure on it to kill any mold and mildew that may be stopping it up at the bottom. Make sure all the water drains out as any left around the drain can start building up the blockage again.

A bare copper wire wrapped around the evaporator near the heater and extended a couple of inches down the drain may keep it from refreezing with the heat convection.