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99 out of a 100 times this issue is because either the vacuum check valve is no good or there is a vacuum leak in the vacuum line that feeds the HVAC controls.
How is the condition of the connector for the resistor? There is a replacement pigtail available with larger wires. It's supposed to take care of an overheating problem with the connector.
If the connector is in good shape, then you might be looking at replacing the blower motor. As it wears it draws more and more amps. This extra draw could burning up the resistors.