Dehumidifiers are traditionally made to also work as refrigerants; they don’t just dry the air automatically. They trap the moisture from the air, condense that trapped vapor to release the dry air. The compressors built in dehumidifiers are meant to keep working under certain temperatures—most units will work at temperatures just above 65 degrees Fahrenheit—anything below this ambient temperature and the dehumidifier starts icing up. It’s normal for a dehumidifier to ice up and you can expect this with most units (I presume these are the units you have been using). Because of dehumidifiers freezing up, manufacturers came up with low temperature dehumidifiers. A low temperature dehumidifier will continue working even when the ambient temperature falls below the specified 65oF. A low temp dehumidifier will work perfectly for your basement. Check our review on the best dehumidifier for your basement here.