Why does the hot terminal of my extension cord always burn out?
Firstly when a plug or socket overheats you should replace BOTH the plug and the socket and also cut-back any heat-damaged wire. Heat damage can cause buildup of poorly conductive materials on contacts and it can cause loosening of the springs in socket contacts. This means that mating a heat-damaged connector with a good connector can cause the problem to spread.
Secondly breakers don't trip the instant a circuit is overloaded and US regulations allow 15A outlets to be installed on 20A circuits. So it is quite possible to overload an extension cord without tripping a breaker. You really need to pay attention to what loads are connected to a cord rather than just relying on breakers.
Thirdly normal domestic plugs and sockets aren't suitable for use in wet conditions. If you are going to leave wiring outdoors then it really needs to be done in a more suitable manner.
I suspect the reason that the hot fails first is simply that it in a normal american plug the hot contact is smaller than the neutral contact.