The only thing that could blow a resistor consistantly would be too much current. I would think the fuse on the fan would blow before the resistor if it was sized properly though.
Do you know the value of the resistor?
Either the fan is malfunctioning and drawing excess current, or could it be jamming on something in there?
Low voltage can also cause high current draw.
As a temporary step, I would replace the fuses with lowest value that doesn't blow in normal operation.
John C.