The metal bits in the plug can be removed by gently lifting the plastic flap retaining them (sometimes by pressing the metal flap down, depends on make) and GENTLY pulling out, or pushing with a pin from below. The connection can then be checked, sorted with a soldering iron if required, and reassembled. It could well be that the receptacle or pin has gained a bit of corrosion or muck or might just need a VERY GENTLE tweak before reassembly to ensure that there is good pressure to make sure of a good electrical contact.
Thats assuming the problem is at the plug end of the wire. If its anywhere else, much depends on the make of ESC. Some you can get at the innards to change the lead, others are seal for life. This means that when it goes wrong, its dead.