Why does your air conditioner only work for the first 3-5 miles and then stops blowing cold air Recharging the refrigerant did not help?

If the AC unit has a condensor check its pressure and make sure that it is working properly with the unit, I.E. condensing the warmer coolant quickly back to a useable form, otherwise recharging the refrigerant is pointless. Also, check your heater valve. It could be that your AC is working fine but when your vehicle gets warmed up then you're heating your nice cool air before you get a chance to enjoy it!