We have a Maytag refrigerator with a bottom freezer. The bottom freezer is not freezing. We have replaced the relay and it still doesn't freeze. There is now frost on the back of the freezer.

What relay did you replace? The most common reason it won't freeze is dirty coils and fan under unit. If the coils are blocked with dirt it cannot move heat out of unit. Also, check the condenser fan. It must turn at the right RPMs and be clean just like the coils have to be clean. Another problem can be that you have an evaporator fan may not be running due to an open fan t-stat or bad fan motor or defrost timer (which will also cause it to ice over and block all airflow and ruin compressor valves). Here is a manual: https://dl.dropboxusercontent.com/u/8010163/Maytag%20Refrigerators.zip