AC Fan Motor keeps burning out, is this common for this year and model

In some vehicles, just because you turn on the A/C..the fan does not come on...and some, when you set the A/C to on, you have to make the fan blow to make the A/C compressor work.. Sounds like,maybe, the blower motor resistor may be bad.. they are easy to change and not too expensive..You should be able to buy one at ( some will install it for you - if you are real sweet) :
http://www.oreillyauto.com/site/c/search.oap?keyword=blower+motor+resistor&year=2005&make=Chrysler&model=Town+%26+Country&vi=5018012
Advance Auto Parts Down for Maintenance
Blower Motor Resistor
Showing Results for blower motor resistor
2005 CHRYSLER TOWN COUNTRY 3 8L V6 Blower Motor Control Module Resistor...

Exactly how to do it is going to depend on your car... Make/model/year is what we nees. Ir's likely behind the glove-box, perhaps above it, though some cars have the fan under the hood. My car required removing the glove box to access it, and spend a couple hours under the dash. The AC hoses were in the way, and we had to purge the AC and pull those first. Hope yours is easier.

I would think either your fan motor is bust. Or it could be a cabling issue.

If you can access the fan motor. Think yours is accessed behind the glove box. Test the fan.

You should be able to get a replacement from a breakers yard.

If not the fan motor is could be a failed switch/speed selector.

Sounds like the fan motor is burned up and drawing too many amps. You will need to replace the motor and the burned up wiring.

How does a 7 year old car get like that?

I have owned many vehicles for 17 to 19 years,
over the past 50 years & never has any of those issues

Only thing I can suggest, is a different shop than you have
used, & limit what your want to spend & repair

blower resistor is common to burn causeing smell. check with dealer, there may be a campain on this problem. if not. replace resistor and harness (pig tail) and blower motor..

The most common cause is a lack of refrigerant. Most systems require a minimum of 2lbs of refrigerant to make the compressor engage. This is a precaution to prevent burning out your compressor. There are leak detection/refill kits available at most auto parts stores. There are also many service stations that are certified in automobile AC systems. Keep in mind, by law, service stations are required to search for and repair leaks prior to recharging your system.

If you have replaced the blower motor resistor block twice all ready, i would be replacing the blower motor itself. When the blower motor is drawing too much current it burns out resistors for lower fan speeds in resistor block, but doesnt blow fuse for fan. Also check for leaves and stuff in fan when removing fan.

Sounds like your heater/bower motor has an issue. Behind the glove box door is your heater motor, and mounted to it is a heater motor resistor. It will have a wire harness plugged into it. These go bad, and you will loose low speeds.

I would think the fan motor is drawing too much current, causing the fuse housing to melt.