loose wires or connections cause increase in resistance which increases current which increases heat ergo, burning the resistor out again...
Jul 10, 2010 Rating
Blower resistor issue by: Certified Service Technician
Sounds like the blower motor may be drawing too much amperage, causing the blower resistor to overheat and fail. I would replace the blower motor as well. As a professional technician in the field, I see this quite often... Hope this helps!