2002 Buick LeSabre blower motor

The blower motor may be drawing more current than it normally should. That could cause the damage to the connectors. Have the current draw for the motor checked. Also, once damage happens like that it is best to replace both sides of the connection. The connections on the blower side may now have extra resistance added to them and that is causing the problem. If the connections are discolored that would be a sure sign of trouble.