When stuff melts it's not from Amp draw...it's caused from high resistance! High resistance will create a "back up" right where the resistive component is and start getting hot. This is why the fuse doesn't blow. While it starts out as a warm spot from the natural amperage it begins to create a bad connection when it cools....much like how and why an exhaust system will rust after a period of time. Then the cycle begins again when it gets used again and again and it will slowly degrade until it reaches the point of failure.
For this reason anything that runs high amperage (15 amps or more...14ga or larger) I will solder my connections for a trouble free circuit. Everything else that can't be OR isn't soldered (i.e. terminal connections, butt connectors and so on...) will get treated with a die-electric silicone grease which cuts down the heat and lubricates the connection which inhibits wear on the terminal from vibration and thermal expansion and reduces any moisture absorption when cooling...much like having an exhaust system ceramic coated. This should solve your problem or if at the very least prolong it for a considerable amount of time! This sounds like a lot more work than you may be used to for doing electrical work but I gaurantee you won't be sorry for taking that extra step when you realize how much more reliable your electrical system is!
