If "keeps going out" means you have replaced resistor, but the same symptom reappeared after a unexpectedly short time of "well. that's fixed"...then my best guess for your problem for a circuit like that would be a overheated connector at the resistor. Installing a new resistor will only "fix the problem" for a short time. Take a close look at that connector for corrosion or melted plastic.
If somehow...which I'll get to... the Resistor Coils are Getting WET somehow, they'll burn out.
That "somehow" could be debris in the HVAC cabinet area, problem with the windshield base cowling drains, the A/C condensate drain, or something rusted, out of place or otherwise damaged. Blower slings water onto the Resistor, or water drips into the Resistor area. Damages Resistor.
Damn my reading comprehension is getting worse- ANYWAY
#4 (med 3) is going bad - you are replacing the resistor card NOT trying to replace or fix the individual resistor?
Then check wiring from HVAC module to resistor or the module itself has problem With med3
Maybe too early to speculate, but I've wondered... Blower Motor is starting to drag, sticky bearings. Could one speed selection work to create the greatest amount of load on that specific coil of the resistor pack?
Common problem when the blower motor does not start rotating instantly when first switched on, is a short circuit. Without a cabin filter, can be a lot of debris build up on that squirrel cage blower wheel, shaft all rusted binding, brushes worn to nothing.
Ha, back in the 70's, could take these motors apart and for 45 cents, replace the bushings and brushes, was nut to hole that wheel on. Now completely throwaway. But back then a new OEM blower motor was only six bucks, so why even fool with it.
Define that blower wheel as a leaf chopper, builds up on the evaporator restricting air flow, sure took them long enough to add a cabin filter.
Would only be happy with an OEM blower, see its 157 bucks at rockauto.com. Outrageous.
Difficult to say without looking at in, seen some packed with chopped up leaves, just needed a cleaning, certainly won't get better. Ebay has a lot of these, some preowned, some aftermarket in the 30-40 range, but just the motor with the wheel attached. Really got teed off at GM when they started heat melting the wheel to the shaft, no way to remove it without breaking it.
May also find your evaporator coated with chopped up debris.
First a nut on a keyed shaft, than a palnut, now this.
Was able to replaced a blower motor with a wheel from my dealer on that 1993 Bravada for 40 bucks, wasn't even safe to drive that vehicle without a blower motor, windows would fog up. but this was about 18 years ago. Keep on making these things cheaper, and the price skyrockets.
Another was peening in ball bearings for the alternator and AC clutch idler pulley and using a press fit that always worked loose, then all these lubricated for life joints, one vehicle was 300 bucks per hub bearings each, pitched it.