If it is taking 1-2 mins to blow you do not have a dead short.
Look at the fuse that has blown, is it melted in a gentle way ot has it exploded black n crispy?
Probably just melted, if that is the case it is an overload.
This would indicate the fan is drawing too much current thus blowing the fuse.
If that is the case it is time for a new fan, or possibly the relay is causing a high current draw because of a bad contact.
I would start by first cleaning all fan connections with contact cleaner and applying silicone grease to them, this will reduce resistance and lower current draw.
Do that and post back with your results.