I saw your discussion previously, but didn't respond at the time because other posters had already sent you in the right direction. By the way just as a forewarning, Shane is not part of the service department, so he could only forward you on to service if you called him direct.
You are burning up your cords because you have a poor connection between the tool's inlet and the plug-it connector on the cord. This results in a high resistance connection and possibly even small arcing at the connector, which in turn causes very high heat. Unfortunately, once this occurs even once, it creates a cascading degradation of the connections (that's true for any electrical plug, not just Plug-it).
The leading cause for this occurrence is not fully tightening the twist-lock on the Plug-it cords. This is the reason why I specifically point this out with a full graphic image in all of my Owner's Manuals. I know that this was mentioned previously, but it is an important enough topic that I want to make sure that everyone reading this thread fully understands it. Some Plug-it cord to tool interfaces are snug enough that when the owner turns the twist-lock, they think that they have fully tightened it, but instead, it is just beginning to hit the detent snap position. The most reliable way to ensure the twist-lock is fully engaged is to note that the twist-lock must rotate a full 90-degrees (1/4-turn).
If I recall, you have already stated that you were positive that the twist-lock was fully engaged. So given the assumption the twist-lock is fully engaged yet you are experiencing overheating problems, then it is quite clear that the electrical pins in the inlet of your sander have been damaged from previous occurrences of high heat. What happens is that once the plastic gets hot and soft, the pins no longer fit their shell as tightly as they should, and frequently, this means they will get pushed back inside of the body of the inlet. In essence, the pins are too short (from getting pushed back) to make full contact with the brass sockets in the plug-it's body.
So the bottom line is that even though you were noticing the damage on your plug-it cord(s), and drawing the conclusion that the multiple plug-it cords were the problem, the actual root cause was the inlet on the tool. Regardless what the cause of the original overheating condition, you now appear to have a damaged inlet on the tool.