I've got a newer model the same at Mike C. Same exact thing. Too bad Razor doesn't do something to remedy this if everyone has the same problem. So based on above I should cut both wires, below the spring coil and through the protective rubber covering both wires? Cut it before the motor and then again at the top? Then use speaker wire to replace it? Does it matter the gauge of the wire? Is Monster wire better? Is it worth trying to tread it back through the spring coil as it doesn't seem to fix the problem. May be easier to just run the wire but buy enough to keep replacing it when it happens again.
I am not sure if running the wire back through the spring is a good idea or not. The spring does not appear to help that much. Its your call whether to use the spring again or not. There is a chance using high strand count wire that the wires will be thicker than the original wires so they will not fit inside of the spring.
I like your idea of replacing the wire without using the spring so it is easier to replace in the future. That gave me an idea to use connectors at each end of the repair so the section of wire that is replaced is like an extension cord with plugs at both ends. Then an extra "extension cord" can be made for a fast and easy repair whenever needed. The type of connectors I am thinking of are the same type that the motor wire already has on its end that looks like this.
ElectricScooterParts.com Item # CNX-50 Connector
I like that idea plus seems easier than trying to get a good connection and soldering the wires back together every time. I'll try this and let you know what I come up with.