If replacing the resistor solved the problem for one day and then the problem returned, I would suspect the new resistor has failed (did you get a genuine ford resistor?). When on the high setting, no resistor is present in the supply to the fan motor, that is why it works for you on high, as you go to the other speeds it switches in different resistors to reduce the current and slow the motor. The problem with a resistor is that as it restricts current it produces heat, heat is what kills a resistor. Ford designed the resistor to run at a certain temperature, if it is failing after 1 day, I would assume that it is getting too hot or was faulty. If it is getting too hot then either you didn't re-install the new one with sufficient heat compound (to aid cooling) or your fan motor circuit is taking too much current and the extra current is causing the resistor to create additional heat which it cant dissipate and this is causing it to fail. I think you need to try and measure the current that the fan motor is taking and see if someone can tell you what is a normal current should be for that motor so you can see if you have an issue with the fan motor. I would also be taking the resistor back to wherever you purchased it and tell them its defective and see if they will replace it whilst it is only a few days old. The longer you wait, the harder it will be to get it exchanged. The shop might even check it before exchanging it and can tell you if it has actually failed.
Gary