You answered your own question; ice boxes should be defrosted every few weeks anyway as the build up of ice actually insulates the temperature sensor and causes the ice to melt. Try turning up (colder) your thermostat, and don't leave your fridge door open longer than necessary. This problem can also occur if your fridge does not get enough rear and side ventilation or if it is situated in a high ambient temperature.
sparky, July 2009